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UNITED STATES OF AMERICA. 



Senior Course 



MECHANICAL DRAWING, 



COMPRISING 



A Complete System of Working Drawings, 

/« / BY / 

'a ^r WILLIAM H. THORNE, 

Director of the Drawing School of the Franklin Institute, Philadelphia, 
Member of the American Society of Mechanical Engineers. 



PUBLISHED BY '# cOPYRiGwr 

WILLIAMS, BROWN & EARLE, T -i*7r/ V 

N. E. Cor. Chestnut and Tenth Streets, Philadelphia/" - *-*!^ 



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Kntered according to Act of Congress, In the year 1890, by 

"WILLIAM H. TRORNE, 
In the Office of the Librarian of Congress, at Washington. 



PREFACE. 

This Senior Course in Mechanical Drawing is the result of my experience 
in making and directing the making of drawings for shop use, and in working and 
directing the work of others from such drawings, combined with that of teaching and 
superintending the instruction of the drawing classes of the Franklin Institute. It is 
essentially practical, without neglecting explanations of the principles involved, ex- 
cepting the dynamical ones, which are beyond its scope. 

Engineering-drawing has been selected as the type of mechanical drawing 
because it has been developed to greater perfection than any other. The working 
drawings of the steam engine are submitted as a model for shop-drawings, to be 
modified by special conditions and circumstances. The subject of Gearing has been 
treated on the basis of actual requirements, without complicating it by abnormal and 
impractical cases. The system of Involute Gear Teeth is presented with the hope 
that engineers will give it their thought, and consider the advisability of adopting 
some one standard for the shapes and proportions of teeth, so that, at some future 
day, a wheel cut in one establishment will gear properly with any wheel of the same 
pitch cut in another. 3 



SENIOR COURSE. 



The student, beginning this course, should be impressed with the idea that the 
way to learn how to draw is to make drawings, and to make them understanding^, 
accurately, and in so finished a manner that the thing could be constructed from & the 
drawing alone without any verbal explanation, and that anything less than this is not 
a mechanical drawing. 

The Plates are reproductions by photographic process of drawings made in 
my usual style, in order not to dishearten the student by the delicacy and perfection 
of line to be found in steel or copper-plate engravings, and characters printed from 
type. 

WM. H. THOENE. 
Gowen Ave., Mount Airy, 

Philadelphia, 1890. 



Table ok contents. 



PAGE 

Introduction, 7 

List of Plates 6 

Helix and Helicoid, Plate 21 11 

Conventional Representation of Screw-threads, ... 18 

Bolts 20 

Steam, Gas, and Water-pipe, 25 

Shop Drawings 26 

Vertical Engine 27 

Listsof Details 28 

Bolts and Keys for Engine, Plate 22, 32 

Piston-rod, Valve-rod, Pins and Rings, Plate 23, . . . 35 

Connecting-rod and Eccentric-rod, Plate 24, 36 

Crank-shaft, Plate 25, 37 

Piston, Shaft Brasses, Gland and Bushing, Plate 26, . 39 

Fly-wheel, Plate 27 40 

Slide Valve and Crosshead, Plate 28 41 

Eccentric and Strap, Plate 29 42 

Brass Details, Plate 30 43 

Covers and Caps, Plate 31, 44 

Steam Cylinder, Plate 32, 45 



PAGE 

Engine Frame, Plate 33, 47 

Construction Drawing of Engine, Plate 34, 48 

Valve Motion, Plate 35, 51 

Bilgram Valve Diagram, Plate 36, 55 

Adjustable Connecting- rod and Eccentric-rod, Plate 37, 65 

Brass Globe Valve, Plate 38 66 

Toothed Gearing, 67 

Involute Gear-teeth, Plate 39, 75 

Approximate Involute leeth, Plate 40 81 

Diametral Pitch, Plate 41 83 

Proportions of Gear-wheels, 85 

Cycloidal Gear-teeth, Plate 42 86 

Bevel Gears, Plate 43, 90 

Conclusion 95 

Table of Decimal Equivalents, 96 

Standard Proportions for Bolts and Nuts 97 

Standard Dimensions of Wrought-iron Pipes 88 

Table for Proportions of Teeth of Gears 99 

Table for Approximate Shapes of Gear-teeth, .... 100 

Index, 101 

5 



List or Plates. 



NO. 

Helix, Helicoid, and Screw-threads, 21 

Bolts and Keys 22 

Piston-rod, Piston-rings, Valve-stem and Pins 23 

Connecting-rod and Eccentric-rod, 24 

Crank-shaft, 25 

Piston, Gland, Bushing, and Brasses, 26 

Fly-wheel, 27 

Slide Valve and Crosshead, 28 

Eccentric and Strap, 29 

Brass Details 30 

Covers and Caps 31 

Cylinder, 32 



NO. 

Engine Frame, 33 

Construction Drawing of Engine, 34 

Valve Motion of Engine, " . . . . 35 

Bilgram Valve Diagram, 36 

Adjustable Connectingand Eccentric-rods, 37 

Globe Valve, 38 

Involute Gear-teeth 39 

Approximate Involute Gear-teeth, 40 

Proportions for Gear-wheels, 41 

Cycloidal Gear-teeth, 42 

Bevel Gear-wheels, 43 



INTRODUCTION. 

If the preceding Junior and Intermediate Courses have been understood and 
the drawings correctly made, the geometry and technicalities and the principles 
of projection should, by this time, be so familiar to the student as to render un- 
necessary any very detailed directions in relation to them. 

The same outfit of tools and materials will be sufficient for this course, except 
that the 5J" Compasses with the lengthening-bar will not describe an arc of much 
more than 12" radius, which is not sufficient for some of the examples of gearing. 
If Beam-Compasses are not available, these examples should be drawn to a reduced 
scale to bring them within the capacity of the 5J" compasses. 

Scales. 

The use of different scales will now become an item of more importance, and a 
correct conception and manipulation of them at the start will prevent much of the 
awkwardness and loss of time so commonly seen in their handling. A full-size scale 



O SENIOR COURSE. 

is a ruler, graduated to units and fractions of the standard of measurement. In this 
country the standard is the foot, subdivided into 12 inches, and each inch is again sub- 
divided into halves, quarters, eighths, and so on. The subdivisions of the inch, on 
scales for drawing purposes, need not be made smaller than -fa", because a sixty- 
fourth, for instance, can be as accurately laid off half-way between two of the thirty- 
second marks as if the sixty -fourth mark was on the scale. These subdivisions of 
the inch, down to -fa should be on every inch throughout the entire length of the 
scale. 

If a drawing is to be made half size, every six inches measured on that drawing 
will be equal to one foot measured on the thing which is drawn, and to efficiently 
make this drawing, a scale should be used whose length was divided into nominal 
feet, each six inches long, and each nominal foot into 12 nominal inches, and each 
nominal inch into nominal halves, quarters, eighths, and sixteenths, throughout the 
entire length of the scale. Although these nominal graduations are only one-half 
the size of the real measurements which their names indicate, they should be read 
and thought of as though they were the full size. So with all other scales, one-eighth 
for instance, in which 1 J" on the drawing is equal to 1 foot on the thing beino- drawn. 
Each \h" on this scale should be marked a foot and considered as such and be sub- 
divided into inches, and each inch into quarters. Although each \" division of the 
scale actually measures only one-thirty-second of an inch, this fact should not be 
thought of, but the distance should be considered as a quarter of an inch. 



MECHANICAL DRAWING. 



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The importance of having the subdivisions of the inches graduated throughout 
the entire length can be appreciated, when the fact is considered, that a large proportion 
of the dimensions on a drawing have to be laid otf so as to come half on one side and 
half on the other side of a centre-line or axis of symmetry, when, if only one foot of 
the scale is subdivided and the measurement exceeds a foot, the scale will have to be 
shifted. This is awkward and consumes time unnecessarily. 

To illustrate the advantage of dividing the length of the scale into feet, and 
each foot into inches, instead of simply marking the inches consecutively throughout 
the length, suppose it is required to lay off the width of some object which is sym- 
metrical about a centre-line, and that this width is 2' 9 J". If each foot is desig- 
nated, a foot mark cau be placed upon the centre-line and the half distance, V 4%", 
be immediately laid off in both directions with a minimum of trouble and chance of 
error. Therefore, in selecting scales, never take any in which only the first foot is 



10 SENIOR COURSE. 

subdivided, nor in which the inches are marked continuously without separation into 
feet. 

Lines. 

The Plates in this Course are drawn with the same conventional lines as in the 
preceding ones; that is, the full lines and short dots represent lines of the object being 
drawn and are to be inked black, the long dots represent centre-lines and important 
bases and lines of reference and are to be inked blue, and the long-and-short dots 
represent construction lines used in obtaining the lines of the object, the preservation 
of which is desirable, and are to be inked red. All dimensions lines are red. All 
red and blue lines are to be full, not dotted. If, however, a tracing of the drawing 
is required for the purpose of obtaining Blue Prints, the lines should all be black and 
be distinguished as in the Plates. 

The size of paper to be used is 21" by 16" with margin lines 20" by 15", the 
same as in the preceding Courses. 



MECHANICAL DRAWING. 11 



HELIX AND HELICOID. 

PLATE 21. 

If a Cylinder is rotated on its axis with a uniform velocity, and a stylus is given 
a uniform motion in a straight line parallel to this axis, the point of the stylus, if 
pressed against the cylinder, will trace a helix upon its surface. The distance which 
the point travels during one revolution of the cylinder, is the -pilch of the helix. 

Draw the top and front views of a cylinder 4" diameter and 3" long as shown in 
the Plate. If this is supposed to be rotated on its axis with a uniform velocity, and a 
point, starting at a, to be moved with a uniform velocity along the line a 6 so as to 
arrive at b at the same time that the cylinder has made one turn, the point will have 
drawn a helix, a c b, of 4." diameter and 3" pitch. 

As the velocities are uniform, it is evident that -when the cylinder has made any 
given fraction of a revolution, the point will have moved the same fraction of the pitch, 
and to draw the projections of the helix it is only necessary to divide the circle, repre- 
senting the circumference of the cylinder in the top view, into any number of equal 
parts, say 24, and the pitch a 6, in the front view, into the same number of equal parts, 
and to project vertical lines from the former to intersect horizontal lines from the latter, 
when these intersections will be points of the helix. 



12 SENIOR COURSE. 

An examination of the location of these points will show that they are symmetri- 
cally distributed to the right and left of the centre-line, and above and below the hori- 
zontal line passing through the point c, which is half the pitch, and that it is therefore 
only necessary to determine one-fourth of the curve. 

In the present case divide the pitch a b, 3", into four equal parts, each £", and 
draw horizontal lines through these four points, then the helix will be at d at the end 
of the first quadrant, at c at the end of the second quadrant, at e at the end of the third 
quadrant and at b at the end of the complete turn, and the curve will be precisely the 
same in each of these four quadrants, only reversed. 

Now divide the first quadrant into six equal parts and determine accurately six 
points of the helix. Select a portion of the edge of an irregular curve which will pass 
through as many of these points, from d towards a, as possible and draw a curve 
through them. Make marks on the irregular curve where it crosses the centre-line 
and outside of the cylinder and draw the same portion of the helix from d towards c by 
placing the irregular curve so as to have the same mark at d, and the mark which was 
at or near a to be at or the same distance from c. Then carry the marks over to the 
opposite side of the irregular curve and go through the same operation, using the oppo- 
site side, from e to c and from e to 6. A small portion of the helix at a, c, and b, can 
often be best made with the compasses. 

To develop the helix, draw the line b b', equal to the circumference of the cylinder, 
12.5664", divide this line into 24 equal parts, erect perpendiculars at each of these 



MECHANICAL DRAWING. 13 

points and continue the horizontal divisions of the pitch to intersect these perpendicu- 
lars, when it will be found that the development of the helix is a straight line from a 
to b' . This must necessarily be so, as b b' represents a uniform revolution of the cylin- 
der and aba. uniform translation of the point. The angle a V b is the angle Avhich 
a tangent to the helix makes with the plane of the base of the cylinder. This sug- 
gests a method of finding this angle trigonometrical ly from a table of natural tangents. 
The length of the circumference of the cylinder is to unity, as the pitch of the helix is 

to the natural tangent of the angle, hence, tangent of the ano;le= - L_ . Make 

° ° circumterence. 

this division and find from the table of tangents the angle corresponding to the quotient. 

This angle will be 13° 25'. 

This development of the helix also suggests a ready and useful method of deter- 
mining any irregular curve that may be desired on the surface of a cylinder, as for the 
production of intermittent motion or varying velocities. The lengths of the divisions 
upon the development of the- circumference represent the velocity of revolution in 
equal times, and the lengths of the vertical lines at these divisions represent the velocity 
of translation of the point in the same times. These can be made anything that may be 
desired and the points projected back to the cylinder. 

Now, inside of this 4" cylinder, draw one 3^" diameter, having the same axis and 
the same length, 3", and upon it draw a helix/, g, h, the development of which will 
befh', making an angle of 17° with the plane of the base. This helix has the same 



14 SENIOR COURSE. 

pitch, 3", as the former one, but the diameter being less, the helix will be steeper, that 
is, a taugent to it will make a greater angle with the plane of the base. 

An examination of the top-view will show that each fraction of the circumference of 
the inside cylinder is on the same radial line as the corresponding fraction of the out- 
side cylinder, while the front view will show that the corresponding fractions of the 
pitch are on the same horizontal lines. If an infinite number of radial lines could be 
drawn in the top-view, they would be projected in the front-view as horizontal lines 
and would constitute the elements of a warped surface called a helicoid, connecting the 
two helices. This is the surface of the ordinary screw thread and is an important one. 
The elements, or lines composing it, need not be perpendicular to the axis but can beat 
any angle. If they are perpendicular, the thread is called a square thread, if at an 
angle, a V thread. Therefore, the warped surface of a screw thread, or a helicoid, is 
generated by a straight line (called the generatrix) moving uniformly along another 
straight line (called the directrix), and at the same time moving uniformly around it, and 
always making the same angle with it. 



The drawing thus far represents two cylinders, one 4" and the other 3 



8 



diameter, with the same base and axis, and with a helix of 3" pitch on each, and 
with the space between these helices representing the surface of a screw-thread of this 
sama pitch.. The 4" cylinder represents the outside diameter of the thread, and the 
3g-" cylinder, the inside or root diameter. It is now necessary to complete the thread, 
for as yet only an imaginary surface has been obtained. Before doing this, however, 



MECHANICAL DRAWING. 15 

an understanding of the purposes and nature of a screw-thread should be obtained. 
Its purpose is essentially to change continuous rotary motion into continuous linear 
motion ; that is to say, if a shaft, having a screw-thread upon its surface, be rotated 
and the helicoidal surface of the thread be made to bear against any object, such 
object will be moved along the shaft in the line of its axis. The distance moved for 
each revolution of the shaft will equal the pitch of the thread. The surface of the 
object, which bears against that of the thread, should coincide with it to the greatest 
extent possible, hence it should be a similar thread wound on the inside of a cylinder, 
called a nut, of a diameter equal to the outside diameter of the screw. The nut can 
be given any desired length so as to contain as many turns of the thread as experience 
or experiment may determine to be necessary. The surface of the screw slides upon 
the surface of the nut in the manner of a spiral wedge, exerting pressure and causing 
motion axially. The greater the extent of this surface, the more will the pressure be 
distributed and the less will be the consequent wear. The greater the pitch of the 
screw, the greater will be the relative motion of the nut. The smaller the diameter 
of the thread, relatively to the pitch, or the greater the pitch-angle, the smaller will 
be the amount of sliding of the surfaces required to produce the motion, and conse- 
quently the less loss from friction. The more nearly perpendicular the generatrix of 
the screw surfaces is to the axis, the less the loss from friction, hence a square thread 
is the most efficient for producing motion, while a V thread is the most efficient for 
holding pieces firmly together, because the friction tends to prevent the thread from 



16 SENIOR COURSE. 

slipping back after tightening. For screws designed to give motion, the pitch-angle 
should be large, but not more than 45°, while for those designed to hold pieces together, 
the pitch-angle should be small. 

In the drawing of the A" screw, one of the helicoidal surfaces or one side of the 
thread was completed, and the next step is to draw the other side. In ordinary square 
thread screws, the width of the thread is made \ the pitch, and the depth -fa the pitch, 
or | the width. In the present case, the depth has been taken as T 7 g-", and therefore 
the width would be \" , which would leave a space between the turns of 2J". This 
space can be utilized by making two other similar threads in it, thus gaining three 
times the amount of wearing surface of a single thread in the same length. This will 
therefore be a screw of 3" pitch with triple thread, each thread will be \" wide and 
T 7 F " deep, or the same as if the pitch was \" instead of 3". When there is more 
than one thread, the combined width of screw and space is called the individual pitch. 
This expression refers solely to the axial measurement of the thread and space, and 
must never be used in mistake for the real pitch, which is the axial distance traveled 
during one turn of the thread. 

In drawing the helices already determined, an irregular curve was used and marked 
to facilitate the reproduction three times of one-fourth of the curve. Now lay off 
distances of \" on lines parallel with the axis, from any points of the original helices, 
which will enable the irregular curve to be located the same as it was for them, and 
complete the curves for all the threads. 



MECHANICAL DRAWING. 17 

An examination of the drawing thus completed, of a square-thread screw, A." diam- 
eter, 3" long and 3" pitch, triple thread, will show how unnecessary it is, after having 
made and understood a drawing of one screw, to go through the tedious operation of 
determining the front view of ordinary screw threads, and how little useful information 
such a view imparts. Now draw a continuation of the screw, 1 \" long, in section on 
the central plane. This will show clearly the shape of the thread and space, and their 
widths and depth, and needs only to be supplemented by the statement that the screw 
is 3" pitch, triple thread. 

The true helices should, however, be carefully and accurately drawn full size in 
this example, in order to obtain a clear comprehension of the subject, because there are 
many cases in which an exact determination of the curves and surfaces is very import- 
ant, as, for instance, in the screw propellor. 

If the underlying principles are fully understood, but little difficulty need be an- 
ticipated with any helicoidal surface. The line in which a section in the plane of the 
axis cuts this surface is the generating line. This line intersects the axis, revolves 
uniformly around it, and travels uniformly along it the length of the pitch for each 
revolution. Every point of the line generates a helix of the same pitch, while the 
line generates a helicoid. The line may be at any angle with the axis, and the helix 
generated by any point of it can be readly projected and developed. 



18 SENIOR COURSE. 

CONVENTIONAL REPRESENTATION OF SCREW-THREADS. 

Instead of drawing the true helices of an ordinary screw-thread, it is as clear, as 
useful, and almost always allowable to represent them by straight lines. 

To illustrate this, draw as in Plate 21, six shafts, each 1" diameter and 4" long, 
to be threaded for 2" of their length with square thread. Let the thread on one pair 
be \" pitch, on the next pair \" pitch, double thread, and on the last pair f" pitch, 
triple thread. The width of the thread, being half the pitch of a single-thread screw, 
will be \ n ', and the depth will be f of this, or ■fe ,t . Therefore the diameter at the 
root of the thread will be f %" . Draw the root diameter. Then lay off \" spaces on 
the outside diameter. Each alternate one of these will be a thread, which will ad- 
vance half the pitch in half a revolution. Therefore draw parallel straight lines, in- 
clined an amount equal to half the pitch, as shown, to represent the outside helices on 
the front surface of the cylinder, and, in the spaces between the threads, draw portions 
of similar straight lines, inclined the same amount in the opposite direction, to repre- 
sent what can be seen of the helices on the back surface. 

By referring to the A." screw, it will be noticed that the helices at the bottom of 
the square thread, begin opposite the beginning of the outside helices and disappear at 
the central plane, therefore draw straight lines from the central plane to these points, 
as shown. 

Even this amount of work is generally considered superfluous in shop-drawings 



MECHANICAL DRAWING. 19 

and one of the three conventional methods shown is usually employed. The upper 
one, in which only a few threads at each extremity of the screw are indicated, and in 
which the root diameter is expressed by dotted lines, is the clearest. The bottom one 
is the simplest and is often sufficient, but in all cases of working drawings of square- 
thread screws, the pitch should always be given, no matter how the threads are drawn. 
The middle one is shown in section, the section representing wrought iron or steel by 
means of a wider space between each three of the lines. This is a conventional method 
of distinction from cast iron, in which the section lines are regularly spaced, as shown 
in the 4" screw. If the material is steel, this word should always be written upon 
the piece. Steel is often represented by dotting the middle one of the three lines, but 
the operation is tedious and the result sometimes uncertain. Thus far, the screws have 
all been right-handed, and a means must now be obtained by which a "rigid-hand 
screw" can always be identified. Take, in imagination, the blank end of a screw or 
the head of a bolt in the hand, with the screw pointing away from the person, insert 
the other end in a nut and revolve the screw so that the top surface moves to the right, 
then, if the inclination of the thread is such that the screw will advance into the nut, 
the screw is right-handed. A " left-hand screw " is the opposite of this. The word 
left-hand should always be Written on the drawing, even if the direction is properly 
shown, as thus : left-hand square thread, 3" pitch. A thread is always presumed to be 
single and right-handed. H otherwise, the information should be written on the 
drawing to avoid mistakes. 



20 SENIOR COURSE. 

It is customary to make the pitch of square-thread screws twice, or the number 
of threads per iuch one-half that of standard bolts, as given in the Table on page 97. 
Therefore, a standard square thread is double the pitch of a standard bolt of the same 
diameter, the thickness of the thread is J, and the depth T 7 g its own pitch. 

The sides of the threads of screws can be given any desired angle and depth, ac- 
cording to their purpose, but there are no universal standards except for bolt and gas- 
pipe threads (to be considered farther on), and for square threads, as above. Numerous 
local standards, such as sharp V threads, half V threads, bastard threads, hydraulic 
threads, etc., are used for special purposes, but it is only necessary to fully consider 
the standards for bolts and pipes, as universally adopted in the United States. 



BOLTS. 



Bolts are round bars with a screw-thread on one end and a head on the other, 
and are used for holding pieces together. They are more largely and universally em- 
ployed in engineering construction than any other single piece. Realizing the im- 
portance of a uniform system for their proportions, Mr. William Sellers, on April 



MECHANICAL DRAWING. 21 

21st, 1864, read before the Franklin Iustitute of Philadelphia, an "Essay on a Sys- 
tem of Screw-Threads and Nuts," which gave the results of his experience, investi- 
gations and experiments, and the proportions which he recommended. This system 
has been adopted throughout the United States, and is known either as the Sellers, 
the Franklin Institute or the United States Standard proportions for Bolts and Nuts. 
The Table on page 97 gives these proportions for bolts from \" diameter up to 3" 
diameter. 

The pitch of the screw is indicated by the number of threads or pitches in one 
inch of length, in order to avoid fractional measurements. A section of the screw in 
the plane of the axis will give what is called the shape of the thread. This shape is a 
V whose sides make an angle of 60° with each other. The top of the thread is cut 
off to make a flat equal to \ the pitch and this same amount is filled in the bottom to 
make there an equal flat of \ the pitch. This makes the depth of the thread equal to 
.65 pitch. Draw the section of a portion of this standard thread 2" pitch, as shown. 
The Bolt Heads and Nuts are made either hexagonal or square, according to their pur- 
pose. Their short diameter is equal to one and one-half times the diameter of the 
bolt plus one-sixteenth of an inch, and their thickness is equal to the diameter of the 
bolt minus one-sixteenth of an inch. By short diameter is meant the perpendicular 
distance between the sides of the hexagon or the square. 

Unfortunately, at the time that this system was originated, the lack of manufac- 
turing facilities seemed to render it advisable to make a different standard for finished 



22 SENIOR COURSE. 

bolt-heads and nuts from that for black ones, in order that the former could be pro- 
duced by cutting ■£$" from each side of the latter, and the standard for the latter was 
made yg- larger than the former to allow for this. The inconvenience of this error 
was soon discovered, and while Mr. Sellers and many other eminent engineers adopted 
and have always adhered to the finished sizes as the standard for both finished and 
black bolt-heads, very many others, including the U. S. Government, adopted the 
black sizes, with the result that as regards heads and nuts there are now two stand- 
ards and consequently a wrench made at one place may be -Jg-" too large or too small 
for a nut made at another place. 

Now draw a Standard Bolt, \" diameter, A\\" long, threaded to 3J 7/ from head, 
with hexagonal nut and with washer. Make, first, a front view, showing the diameter 
and length of the bolt, the short diameter and thickness of head and nut (which will 
so far be simply rectangles), the diameter and thickness of the washer (in section), 
and the standard thread dotted within the nut and with the helices represented by 
straight lines on the part outside of the nut, but do not dot these conventional helices 
within the nut. A good method of procedure, in drawing this standard V thread, is 
to mark off spaces equal to the pitch on one side of the cylinder and one mark on the 
opposite side equal to half the pitch or midway between any two of the former. Then 
draw parallel lines, with this inclination, across the cylinder to represent one of the 
outside helices. Lay off the root diameter, and draw lines for the root cylinder. 
Draw 60° lines from where the helices already drawn touch the outside cylinder to 



MECHANICAL DRAWING. 23 

the root cylinder, but only on one side of the thread. Then draw 60° lines for the 
other side of the thread, setting the triangle so that the lines will leave equal spaces at 
top and bottom of thread. This will give all the points for the completion of the rest 
of the conventional helices, those for the bottom of the threads having greater incli- 
nation than those for the top. 

Next make an end view, showing the circles of the diameters of the washer and 
bolt. The root of the thread is conventionally shown by a circle of the root diameter, 
one-half of which is a full line and one-half dotted. 

It now remains to complete the head and nut. These will be hexagonal prisms 
J-J" long with short diameter 1 T V'- Draw the hexagon in the end view and from 
this the projections of the sides in the other views. The corners of the outside ends 
of the head and nut are not left sharp but are beveled off, or chamfered as it is called, 
and the resulting shape is that of the intersection of a hexagonal prism with a cone 
having the same axis. 

To determine this cone, draw, in the front view, aline at 45° with the axis, that 
will cut off about ^" from the corner of the nut. Where this line cuts the axis will 
be the apex of the cone. Draw its other side, project the apex to the top view and 
draw the cone there.. The lines of intersection of the nut with the cone will be hyper- 
bolas, which can be approximated by arcs of circles. The tops of these arcs will be 
determined by the intersection of the sides of the nut with the cone in the front view, 
and their extremities by the intersection of the corners of the nut with the cone in 



24 SENIOR COURSE. 

the top view. Draw lines across both views from these intersections to determine the 
points of the arcs and find centres by trial from which to describe them. 

The constant recurrence of bolts in Shop-drawings makes it desirable that they 
should be represented in as simple a manner as possible. This is accomplished by 
omitting the V of the thread entirely and merely drawing inclined, fine, parallel lines 
of about the proper inclination and at about the distance apart of the helices of one of 
the external edges of the thread, as shown. Only one view, showing the length of the 
bolt, is given, and that is on a plane perpendicular to two sides of the head. The 
chamfer of the head and nut is indicated by arcs, tangent to the extreme ends of the 
head and nut, described with a radius equal to about f their thickness. An end view, 
showing the hexagon, may be made, but is not essential. The washer should always 
be shown in section, as by this means the fact that it is a separate piece is emphasized. 

Draw the same bolt in this manner, alongside of the other one, to demonstrate 
that this conventional method gives sufficient directions for the construction of a stand- 
ard article which is being continually reproduced. 



MECHANICAL, DRAWING. 25 

STEAM, GAS, AND WATER PIPE. 

Pipes are made by bending strips of wrought-iron into long cylindrical tubes 
and welding the seam by means of a special furnace and machinery. Screw-threads 
are cut on each eud to fit corresponding threads on the inside of the fittings, but the 
cut is tapering, that is to say, the helices are described on a cone instead of a cylinder. 
This enables the screw to be easily entered in the nut, and at the same time permits a 
very tight joint to be made without great accuracy in their relative diameters. The 
thread is a sharp V, its outside diameter being smaller than that of the pipe at the 
extreme end. This diameter gradually increases and the thread disappears. The 
taper is f" to the foot, or, in other words, the cone, if produced, would increase 
\" in diameter for every foot of its length. 

There is a great discrepancy between the nominal and actual inside diameters of 
wrought-iron pipes, due to a want of proper means of manufacture and of knowledge 
of their required strength, at the time when their use was begun. The standard for 
outside diameter and pitch of thread, which was first adopted, has been adhered to, in 
order to maintain interchangeability, while improvements in manufacture aud a better 
understanding of the conditions have enabled thinner iron to be used, and the inside 
diameter has been correspondingly increased. 

The Table on page 98 gives the standard proportions for pipes, as used in the 
United States. 



26 SENIOR COURSE. 



SHOP DRAWINGS. 

Among all the constructive trades or mechanic arts, there is none in which the 
variety of operations, the multiplicity of detail, the accuracy of measurements, the 
mathematical calculations, the scientific requirements, and the harmony and unity 
essential in the work of a large number and variety of skilled mechanics and engi- 
neers, are so great as in machine construction, and the great secret of the efficiency of 
the modern machine shop in producing original and intricate machines at reasonable 
expense and with successful results, lies in the system of working drawings which is 
employed. The study, therefore, of such working drawings cannot fail to be of 
benefit to any one desiring to express and record mechanical ideas relating to any con- 
structive art. 

As the Steam Engine is an interesting machine and one whose parts are compara- 
tively few and familiar, it has been selected for the purpose of making a complete set 
of such drawings, sufficient to enable every detail to be constructed and the whole to 
be assembled and erected. The type will be a small vertical engine with steam 
cylinder G" diameter, having a piston stroke of 8", single eccentric, plain D slide 
valve, and all the parts as simple as possible. The subject will be approached, not 
with the view of designing the engine, nor of investigating the principles of steam 
engineering involved, but merely of making the drawings necessary for its construe- 



MECHANICAL DRAWING. 27 

tion. Therefore, it will be assumed, in the first place, that the proportions have been 
calculated, the form determined and the complete construction-drawing finished by a 
competent man, and placed in the hands of an apprentice for the purpose of having 
separate drawings made of every piece, which would enable a number of workmen 
to perform independently and at the same time harmoniously, the various operations 
necessary. When all the detail-drawings are finished, a construction-drawing will be 
made, such as would enable these details to be properly assembled and the complete 
engine to be erected. 



VERTICAL ENGINE. 

When the designer has completed his construction-drawing, , he should make lists 
of all the different pieces comprising the engine, giving to each piece a number and a 
definite name, by which it can always be identified. This will prevent the confusion 
which is sure to arise when any latitude is allowed in the naming of the details. 
One name, even if unsuitable, is preferable to two appropriate ones for the same 
piece. 

The lists for the 6" by 8" Vertical Engine shown by Plate 31 are as follows : 



2a 



SENIOR COURSE 



LISTS OF DETAILS. 



LIST OF IRON CASTINGS. 



-No. 1.— Frame, Plate 33 



2.— Cylinder, " 

3. — Steam Chest Cover, ...... " 

4. — Cylinder Head, " 

10.— Slide Valve, « 

11.— Piston, « 

12.— Front Cap, Crank Shaft, ... " 



32 
31 
31 
28 
26 
31 



-No. 13.— Back Cap, Crank Shaft, . . . Plate 31 

- " 16. — Eccentric, " 29 

• " 17.— Top- Half of Eccentric Strap, " 29 
■ " 18.— Bottom Half Eccentric Strap, " 29 

- " 19.— Fly Wheel - . . "27 



20. — Cresshead, 



28 



LIST OF BRASS CASTINGS. 



-No. 5.— Gland in Cylinder, Plate 26 



2- 
2- 
1- 



6. — Bushing in Cylinder, 

7.— Stuffing Box for Valve Stem, 

8 — Nut on 7, 

9.— Gland in 7 

14. — Front Brass for Crank Shaft, 
lo— Back Brass for Crank Shaft, 
21.— Upper Brass in Conn. Eod, . 



26 
30 
30 
30 
26 
26 
30 



1-No. 22. — Lower Brass in Conn. Rod, . 
1- " 23. — Bushing in Connecting Rod, . 

3- " 24.— Oil Cup with straight outlet, . 

4- " 25.— Oil Cup with side outlet, . . . 
7- " 26.— Oil Cup Cover, . 

3- " 27.— Oil Tubes 

4- " 28.— \" Standard Brass Nut on 

Valve Stem, 



Plate 30 


a 


30 


it 


30 


u 


30 


tt 


30 


it 


30 



30 



MECHANICAL DRAWING. 



29 



LIST OF FORGINGS. 



1-No. 500.— Crank Shaft 

1- " 501— Connecting-Rod, 

1- " 502.— Eccentric Rod, 

1- " 503.— Piston Rod, 

2- " 504.— Piston Ring, . 

■Valve Stem, 

•Crosshead Pin, 

■Valve Stem Pin, 

4- " 508.— Stud Bolt for Caps to Frame, 

Black 

10- " 509.— Bolt in Cylinder, ..... 



1- " 505, 
1- " 506, 
1- " 507, 



Plate 25 


it 


24 


u 


24 


il 


23 


t( 


23 


ii 


23 


(( 


23 


It 


23 


u 


22 


u 


22 



2-No. 510.— Stud Bolt in Cylinder, Bind; Plate 22 

2- " 511.— Round Head Bolt in Con. 

Rod, , "22 

10- " 512.— Stud Bolt in Steam Chest, 

Black "22 

2- " 513— Stud Bolt for Cyl. Gland, 
Black, 

2- " 514.— Round Head Bolt in Eccen- 
tric Strap 

1- " 515.— Steel Key in Eccentric, . . 

1- " 516.— Steel Key in Fly Wheel, . 



In order to readily recognize forgings, their numbers begin at 500, and any num- 
ber below 500 must therefore be a casting. These numbers should be put on the 
corresponding pieces in the Construction Drawing in red ink to aid in identifying the 
parts when the machine is assembled, and to be obviously distinct from the dimen- 
sions. 

Having now the Construction Drawing and the Lists, it is required to make 
Detail Drawings, showing each piece separately. Good judgment and experience are 
required in selecting and distributing the pieces on such drawings, so as to keep 
together as much as possible those requiring similar operations to be performed upon 



30 SENIOR COURSE. 

them, and thus avoiding demands for the same drawing from different persons at the 
same time. 

The detail sheets should be of uniform size and not too large for convenient handling. 
The printed plates in this Course are the same size as in the preceding, namely, 5 inches 
by 3|- inches within the margin lines and should be drawn on sheets either lt)£ inches 
by 8 inches, in which case the scale would be double, or 21 inches by 16 inches, in 
which case the scale would be four times that of the printed plates. 

The lines should be inked in the same manner as heretofore, that is, all lines 
representing the pieces themselves should be black, the circles and curves being inked 
first and shaded at the same time, then all the fine and dotted lines and then the heavy 
shade lines. After all the black lines on the sheet are finished, the centre lines, repre- 
sented by long dots in the plates, should be inked blue but not dotted, and then the 
dimensions lines made in red. All lettering and figuring should be black, except the 
list numbers, which are more distinct if red. Put in the dimension lines and figures 
directly in ink without previous pencilling. This is readily accomplished, saves time, 
and avoids unnecessary erasures. Put the number of the Plate always in the same 
place and the title always in the lower right-hand corner of the sheet as it lies length- 
wise. This enables any desired one to be readily found among a package of them, 
and is a great advantage over the bad method of placing the title wherever there 
happens to be room for it or where it will look the best. Never finish a drawing or 
even a sketch without putting your name and the date upon it, as these are never 



MECHANICAL, DRAWING. 31 

useless and frequently are of great value in tracing the history of a machine and in 
establishing the priority of an invention. 

The theory of orthographic projections, which has already been fully treated in 
the Junior and Intermediate Courses, must be strictly adhered to in the practical appli- 
cation which is now to be made of it, and the different views that are essential to a 
clear comprehension of an object must be arranged in accordance with this theory, and 
never misplaced for convenience in drawing when there is any risk of a consequent mis- 
understanding. Such conventionalities and abbreviations as are clear and unmistak- 
able and the omission of such views as do not give additional necessary information, 
are not only allowable but also desirable. The purpose to be kept constantly in view 
is to give all information necessary to enable the thing to be constructed, with the 
least risk of causing misunderstandings and errors, and to give this information in 
the clearest and simplest manner possible. 

The detail plates are arranged progressively, beginning with the smallest and 
simplest forgings and ending with the Engine Frame, so that every piece can be 
understood before the construction drawing of the Engine is made. 



32 SENIOR COURSE. 

BOLTS AND KEYS FOR ENGINE. 

PLATE 22. 

Make a detail drawing of all the Bolts and Keys of 6" by 8" Engine shown 
on Plate 34. 

The Caps over crank-shaft bearings are held by two f " stud-bolts for each cap. 
A stud-bolt has no head. It is threaded on both ends, one of which is screwed into 
the stationary piece a distance equal to one and one-half times its diameter and the 
other has a standard nut upon it for the purpose of holding the movable piece. Stud- 
bolts are used in places where through-bolts cannot be, and where the piece that is held 
by them has to be occasionally removed. They are preferable, for this purpose, to 
Tap-Bolts, as an ordinary bolt is called, which passes through the movable piece and 
is screwed into the stationary piece. A through-bolt, called simply a bolt, is one which 
passes through both pieces. When a bolt is required to fit accurately and thus pre- 
vent any possible lateral movement, the through-bolt is the best. When this cannot 
conveniently be used, the stud-bolt should be, because, when once fitted to place, it 
need never be removed and thus all wear and change of alignment is avoided. If, 
however, two pieces are bolted together permanently, the tap-bolt will serve the pur- 
pose. 

Find the length of the f " Stud-Bolts required to hold the caps and draw one as 



MECHANICAL DRAWING. 33 

shown, with a nut on one end, the threads indicated, and the dimensions marked. 
No dimensions are required for the nut, as this is a standard article, presumed to be 
made in quantity and taken out of stock. The thread upon the end which screws 
into the casting is \\" long, or 1J diameters, while that upon the other end is some- 
what longer than the thickness of the nut, to allow draught. The total length of the 
bolt should always be given to save calculations in the shop, but the allowance for 
rounding and finishing the end should be left to be determined by the method of 
manufacture. 

Draw, in like manner, the two f " stud-bolts in the cylinder. The length of 
these is made up of the distance to which they are screwed into the cylinder, ff", the 
thickness of the flanges through which they pass, f", and the thickness of the nut, 
■fe" — a total of 2 \". As they do not fit the holes, there is no necessity of their 
being finished, and they should therefore be marked black. This is the only distinc- 
tion required between a forging which is to be used as it comes from the smith and 
one which is to be tooled and finished all over. The drawing in both cases is the 
same. When no note is made the piece is to be finished all over, when marked black 
it is not to be finished at all. If certain parts of it are to be finished and the rest left 
black, put the letter /across the lines representing the finished surfaces or draw long- 
and-short dots parallel and close to these lines. 

Now group together all the rest of the bolts and also the keys required for 
the Engine and draw them as shown on Plate 22. The bolts numbered 511 and 514 



34 SENIOR COURSE. 

have round heads. The diameter of a round head is one and one-half times the diam- 
eter of the bolt. The thickness of the head is one-half its diameter, neglecting thirty- 
seconds. 

The large number and variety of bolts required in building machines frequently 
make the drawing of them a very tedious operation and form an inducement to abbre- 
viate as much as possible. Their standard character and the familiarity of the work- 
man with their manufacture, render this abbreviation possible and desirable. In 
- Plate 22, the end-views could be dispensed with altogether without detriment ; or, 
instead of a drawing, a list could be made, giving the kind, diameter, and length of 
bolt, the kind, diameter, and thickness of head, the length of thread and the place 
where the bolt is to be used, as thus : 

4— No. 508. Stud Bolt, f " dia., 2|i" long, with ends cut l\" and |". For Caps 
to Frame. 

10 — No. 509. Black Bolt, §" dia., 2 T V long, with end cut to l^V' from head. 
Black Hex. Head, V dia.. ~V thick. In Cylinder. 

2 — No. 511. Round Head Bolt, f" dia.. 3 T V' long, with end cut to 2i|" from 
head. Round Head \^" dia., \" thick.' In Connecting Rod. 

1 — No. 516. Steel Key, \" square, 5" long, one end rounded. In Fly Wheel. 

The pitch or number of threads of bolts need not be mentioned unless it differs 
from the standard. 



MECHANICAL DRAWING. 35 

PISTON ROD, VALVE ROD, PINS, AND RINGS. 

PLATE 23. 

Proceed now to make working-drawings of the forgings, beginning with the 
least complicated and arranging them judiciously, as shown in the Plate. Notice that 
there are no dimensions on the nuts, because they are standard and no information is 
required. They might be omitted entirely. The taper of the Piston Rod is indicated 
by giving the diameter of the large end only of the taper part and expressing the 
amount of reduction to be given the diameter per foot of length. The Split Pin, 
which is used to prevent the possibility of the nut backing off and releasing the Piston, 
need not be figured except for diameter, because it is a standard article of commerce. 
The small hole shown in the Valve Stem Pin is for a split-pin. The holes in the 
Crosshead Pin are for oil, the longitudinal one being tapped, 16 threads per inch, to- 
receive an Oil Cup, No. 25. The Piston Rings are of the Ramsbottom type, made of 
steel, bored -jfo" too large, and have the ends finished at an angle with the plane of the 
axis and sufficiently apart to permit of springing together and turning the outside 
diameter to fit the 6" bore of the Cylinder. They then possess enough elasticity to 
preserve a steam-tight fit without causing undue wear. The nuts on the Valve Stem 
are made of Brass to prevent them from rusting fast. They are standard and require 
no dimensions. 



36 SENIOR COURSE. 

CONNECTING ROD AND ECCENTRIC ROD. 

PLATE 24. 

The Connecting Rod is of a very simple type. The crosshead end is spherical, 
bored to receive a brass bushing and faced off to fit the crosshead. The crank end 
has a flange with holes for the bolts to hold the brass boxes. It has. a longitudinal 
oil hole drilled to meet a radial one which is tapped for an oil cup, No. 25. The axis 
of the radial oil hole is also the axis of a spherical swell made in the rod to add metal 
and strength. As there is not sufficient room on the paper for the entire length of the 
rod, the ends are drawn complete and the middle part is shown as though broken. 
This is a very useful device and possesses no disadvantages. Care must, however, be 
taken in drawing broken taper pieces, such as this one, to preserve the actual taper. 
No difficulty need be apprehended if it is remembered that a part has been taken out 
of the centre and the ends brought closer together. 

The Eccentric Rod has its end in the form of a similar flatted sphere and is also 
shown broken at the centre. 

These breaks are represented as an irregular fracture and are section-lined to 
represent wrought-iron ; that is, with three lines at 45°, then a wide space and then 
three similar lines, and so on. A wide space between each set of three lines is the 



MECHANICAL DRAWING. 37 

conventional method of representing wrought-iron and steel, but in all cases where 
steel is intended, the word steel should be added to the title of the piece. 



CRANK SHAFT. 

PLATE 25. 

The Crank Shaft is of the type called double-crank, in which there are two arms, 
connected together.by the crank-pin, and dividing the shaft into two portions, which 
are fitted to the bearings in the main frame or housing of the engine on both sides of 
the crank. The shafts, the ends of the arms, the bosses and the pin are turned, fillets 
being made at the junction of the pin with its bosses and at the junction of all the 
bosses with the arms. The arms are then planed and slotted to the required dimen- 
sions. The curves produced by the intersection of the flat edges and cylindrical ends 
of the arms with the fillets of the bosses are shown in the front view. These curves 
should not be guessed at but correctly obtained for the benefit of the practice to be 
derived from the process. To do this, pass through the bosses, in the front view, 
planes perpendicular to the axis, and draw the circles in the side-view of the traces of 
these planes on the circumferences of the bosses. Project the points, where these circles 



38 SENIOR COURSE. 

cut the edge of the arm in the side view, to the corresponding planes already drawn 
in the front view, for the points of the curves. The fillets of the crank-pin are for 
strength, and those of the bosses for appearance and facility of cleaning. The object 
of extending the arms to the same distance below as above the axis and of making 
them tapering, is to obtain as much weight opposite the crank-pin as is possible, con- 
sistently with convenience of manufacture, for the purpose of counterbalancing the 
opposite parts of the crank together with the connecting rod and the reciprocating 
parts of the engine. Any additional counterbalance that may be desired can be placed 
in the Fly-wheel and will be shown farther on. 

One extremity of the shaft is fitted to the Fly-wheel and the other to the Eccen- 
tric, key-seats of proper width and depth for the reception of the keys for holding 
these pieces being shown. These keys are not, in the same plane, but their centre 
lines make the proper angle with each other to produce the required angle of advance 
of the Eccentric. This will be explained when the valve motion is investigated. 

All the forglngs having now been drawn, the castings will next be treated in the 
same manner ; that is, each piece will be drawn separately and the several pieces 
grouped together on sheets. 



MECHANICAL DRAWING. 39 

PISTON, SHAFT-BRASSES, GLAND AND BUSHING. 

PLATE 26. 

The Piston is a disc of cast iron, 6" diameter and 1" thick, with two grooves in 
its circumference to receive the steel rings. These grooves are deeper than the thick- 
ness of the rings, to allow the latter to be free to move radially and keep in close 
contact with the bore of the cylinder. The sides of the rings should fit closely, with- 
out binding, to the sides of the grooves. The taper hole in centre of piston has its 
size marked only at the large end, the taper being given in the same way as has 
.already been shown on the piston-rod. 

The Brass Bushing is in the lower end of the cylinder and forms a rubbing surface 
for the piston-rod. The Brass Gland is used to compress the packing in the stuffing 
box to prevent leakage of steam around the piston-rod. These pieces are made of 
brass to avoid the rusting and sticking which would result if cast iron was used. 
They are shown in section and the kind of metal is indicated by the spaces between 
the 45° section lines, a wider space between each set of two lines indicating brass. 
The word brass should, however, always be used in addition to the characteristic sec- 
tion. 

The Brass Boxes for crank shaft are made in halves in order to permit them to 
be brought together to take up any lost motion arising from wear. The top and 



40 SENIOR COURSE. 

bottom boxes of each pair are alike, excepting that the top one has an oil hole ; there- 
fore but one of each need be drawn if the fact of the holes is properly noted as 
shown on the Plate. 



FLY-WHEEL. 

PLATE 27. 



The Fly-Wheel is a pulley with six arms and a hub bored to fit the crank shaft. 
The outside (called the face of the pulley), instead of being cylindrical, is in the form 
of two similar cones joined at their bases in the central plane of the wheel. The 
amount of taper of these cones is given as shown on the Plate, namely, |" reduction 
in diameter for each foot of length of the cone. This is called high-face, and is for 
the purpose of preventing the belt from slipping off sideways, and to cause it to track 
properly on the wheel. The inside face of the rim and the outside of the hub are 
similarly tapered to facilitate the withdrawal from the mould, of the pattern from 
which they are cast. The thick part of the rim does not extend the full width, in 
order that the part of it which will come opposite the crank-pin may be still further 
thickened to any desired amount for the purpose of a counterbalance, while the thin 



MECHANICAL DRAWING. 41 

part can be finished and made to coincide exactly with the plane of revolution. The 
key-seats in the crank-shaft and the fly-wheel must be so located in reference to the 
counterbalance that the centre of gravity of the latter will be exactly opposite the 
centre of the crank-pin. 



SLIDE VALVE AND CROSSHEAD. 
PLATE 28. 

The Slide Valve is of box-shape with circular top and flanges at the edges. It 
has a boss extending its whole length with a hole cored through it for the valve-rod. 
The hole is elongated to allow for wear and refitting of the valve without disturbing 
the alignment of the rod. The fuuctions and operation of this valve will be explained 
after the working drawings are completed. 

The Crosshead is tapped to fit the piston-rod, the latter being prevented from 
backing out by a jam-nut. It is turned to fit the guides iu the main frame, and is 
bored to receive the pin for the connecting-rod. 

The sectional views represent cast-iron by means of equidistant lines at 45°. 



42 SENIOR COURSE. 

ECCENTRIC AND STRAP. 

PLATE 29. . 

The Eccentric is a disc of cast-iron bored to fit the front end of the crank-shaft. 
The outside diatnetor is a cylinder whose axis is parallel with, but at a distance of f " 
from the axis of the bore. This distance is the eccentricity and twice this, or \\", is 
the motion produced by one revolution, called the throw of the eccentric. An eccen-. 
trie is really a crank-pin which is larger than the shaft. The outside cylinder has a 
groove at each edge to fit corresponding projections on the inside of the strap, in order 
to keep the latter in place. The key -seat must be exactly central with a line joining 
the two centres so that the angular advance can be correctly fixed by the proper loca- 
tion of the corresponding key -seat in the crank-shaft. 

The Eccentric Strap is made in halves, held together by two close-fitting, round- 
head bolts and bored to fit the circumference of the eccentric. It is tapped to receive 
the eccentric rod and also an oil-cup, located at an angle with the vertical centre-line. 



MECHANICAL DRAWING. 43 

BRASS DETAILS. 

PLATE 30. 

The Connecting-Rod Brasses are made in halves, bolted together, bored and the 
corners rounded to fit the crank-pin. The bolts pass through the two boxes and the 
flange on the end of the connecting-rod. The oil hole in the upper brass coincides 
Avith the one in the rod. Another type of connecting-rod and eccentric-rod is given 
on Plate 35. 

The Stuffing- Bo.v for Valve Stem is bored to fit the stem, the bore being enlarged 
at one end to receive the packing and the gland for compressing it. A thread is cut 
on the outside of this end to receive a nut for forcing in the gland. The other end 
is turned and threaded to fit the hole in the steam chest into which it is screwed by 
means of a wrench fitting the hexagonal collar. It is made of brass, as are all the 
details on this Plate. 

The Gland for stuffing-box has a flange to facilitate its removal. 

The Nut on stuffing-box is threaded inside to fit the latter, and has notches on its 
outside circumference to enable a spanner-wrench to be used for screwing it up. 

The Bushing in connecting-rod is forced tightly into th'e latter while its bore is 
made to work freely on the crosshead-pin. It prevents rubbing contact between two 
similar metals, and can be easily replaced when worn. 



44 SENIOR COURSE. 

The Oil Cups with straight outlet are threaded to fit the holes they are intended 
for, and have hexagonal collars for a wrench. They are arranged for separate tubes 
to be driven in. 

The Oil Cups with side outlet have round collars, as a wrench is not needed for 
screwing them in place. The tubes are of one piece with the cups. 

The Oil Cup Covers are threaded to fit the inside of the cups. Their tops are 
portions of spheres. 



COVERS AND CAPS. 

PLATE 31. 

The Steam Chest Cover is a flat plate with holes for the stud-bolts. These bolts 
are black, as already shown, and the holes are -fa" larger than the bolts, nicety of fit 
not being required. A piece of sheet-rubber, of the shape of the steam-chest flange, 
is placed between the cover and flange to make a steam-tight joint. The cover is 
made thicker and planed at this place, and is planed and polished on the outside face 
and edges for appearance. 

The Cylinder Head is fitted to the counter-bore and flange of the Cylinder, and 
its flange is polished on the outside face and edge. Its bolt holes are also ■&■" larger 



MECHANICAL DRAWING. 45 

than the bolts. The socket at the centre is to provide clearance for the nut on the end 
of the piston-rod. 

The Caps for Crank Shaft are planed on two sides and two edges. On the 
other edges are segments of bosses, the centres of which coincide with the centre of 
the crank shaft. The bolt holes are the same size as the bolts, the latter being fin- 
ished and acting as Dowel-pins to prevent lateral motion. Oil holes are drilled 
through the centre of the caps to match the holes in the brasses, and are tapped to 
receive oil-cups. 



STEAM CYLINDER. 
PLATE 32. 

The Cylinder is the most intricate casting in the engine, and should be carefully 
drawn and thoroughly understood. The bore is 6" diameter for a length equal to the 
stroke, 8", plus the thickness, 2", of the piston, minus an amount which will permit 
the piston-rings to slide a little over at each end of the stroke (in this case |") to 
prevent a ridge being caused by wear. Beyond this length the bore is increased to 
65", for a distance at each end sufficient to allow T V' clearance between the piston 
and heads. At the bottom end this diameter is made by the core, while at the top 



46 SENIOR COURSE. 

end it is bored to facilitate the entrance of the piston, and to fit the cylinder-head. 
The bottom end of the cylinder has a circular boss fitting a hole in the top flange of 
the main frame. This boss is continued in oval shape to make sufficient depth for 
the stuffing-box, and to receive the stud-bolts, No. 513, for the gland, No. 5. The 
stuffing-box is contracted next the bore of the cylinder to form a shoulder against 
which the flange of the bushing, No. 6, is forced. The steam chest is a rectangular 
box with flanges to match the cover, No. 3, in which flanges are tapped holes for the 
stud-bolts, No. 512. The chest is wide enough to receive the slide-valve, No. 28, 
and has finished strips matching the side edges of the latter, and has four bars form- 
ing the valve seat, to which the valve is accurately bedded to make a steam-tight 
joint. The central space between the two inside bars is the exhaust port, through 
which the steam passes to the atmosphere, while the spaces between the inside and 
outside bars are the steam ports, through which it passes to the ends of the cylinder. 
A boss is placed centrally on the side of the chest, having a hole communicating with 
the exhaust space and tapped for a 2" exhaust pipe, while a short boss on the top of 
the chest is tapped for a 1J" pipe for the live steam. At the bottom of the chest is 
an internal boss, bored and tapped to receive the valve-stem stuffing-box, No. 7. The 
centre of this must be at such a distance from the centre of the bore of the cylinder 
as to bring it in line with the centre of the eccentric, when in position on the crank- 
shaft. Through-bolts hold the cylinder to the frame and the head to the cylinder, 
except where the steam-chest prevents their use and compels stud-bolts to be substi- 



MECHANICAL DRAWING. 47 

tuted. Holes for draining off the water of condensation are drilled and tapped for 
\" gas pipe at the bottom of the cylinder, the steam-chest and the exhaust space, and 
bosses are provided for this purpose, as shown in the Plate. The tapped holes are 
shown by drawing the V's to indicate the threads, the number of threads not being 
given, because they are all standard. The "section on line AB," which is shown in 
the Plate, might be dispensed with, as the only additional information which it con- 
veys is that given by the vertical section through the inclined portion of the steam 
port, showing that the latter is straight and not curved, and this might be left to the 
discretion of the pattern maker. 



ENGINE FRAME. 

PLATE 33. 

The Frame has a circular flange at the base and at the top. Its shell is bottle- 
shaped with a long opening in front and behind, to give access to the working parts 
inside. This opening has an external flange all around it, to add stiffness and improve 
the appearance. The seats for the crank-shaft bearings are planed to fit them and are 
tapped for the stud-bolts to hold the caps. The round bosses on the ends of these 



48 SENIOR COURSE. 

seats are concentric with the axis of the shaft and match those on the caps. The 
seats are connected by ribs with an internal circular flange below them. The top 
flange is bored and faced to match the cylinder and bolt holes are drilled in it for the 
cylinder bolts. The guides for the crosshead are bored at the same time. Oil holes, 
for which bosses are provided, are drilled and tapped for Oil Cups No. 25, at the 
upper end of the guides. The shape of the curve of the shell is determined by the 
diameters at the several horizontal planes taken at the given distances apart. The 
widths of the openings are determined in the same manner. The flange around the 
openings projects f " from the exterior all around. The projections of these openings 
in the side elevation furnish a good opportunity for the student to utilize what he has 
already learned about projection. 



CONSTRUCTION DRAWING OF ENGINE. 

PLATE 34. 

This is a drawing of the complete Engine. It is commonly called the Construc- 
tion Drawing and is the original one made in designing the engine. The student 
should not simply copy it, but should construct the different parts in a logical, sys- 
tematic manner, as nearly as possible in the natural sequence that would be followed 



MECHANICAL DRAWING. 49 

by the designer. The Plate is to a scale of f " to a foot, or one-sixteenth, and conse- 
quently many of the small parts and dimensions are obscure, so that in some cases 
reference will have to be made to the detail drawings. 

It is preferable to use a scale of 6 inches to the foot (half size), if the student is 
provided with facilities for doing so. This would require a sheet of paper 42" by 
32". A scale of 4" to the foot would require paper 28" by 21", while a scale of 3" to 
the foot would take 21" by 16", the standard size used in this and the preceding 
courses. The latter scale would not be objectionable if the others are impracticable. 

Detailed instructions in the method of procedure would be very prolix and con- 
fusing, but a general outline maybe given with advantage. In the sectional side-view, 
locate the bore of the cylinder Avith the piston at the top of its stroke, put in the 
flanges of cylinder and frame and the stuffing-box and piston-rod with its attachment 
to the crosshead. Locate the crosshead-pin and from its centre lay off the length of 
the connecting-rod to determine the centre of the crank-pin, from which lay off the 
throw of the crank for the centre of the crank-shaft. Draw in the crank and shaft 
complete and project them to the front view with the bearings and seats. Draw in the 
front-view of the crosshead and the length of the guides, proportioning them so as to 
clear the oscillations of the connecting-rod. Lay off, in the side-view, the thickness 
of the eccentric, the centre of which will determine the centre of the valve-stem, from 
which the plane of the valve-seat can be obtained. Lay off the steam and exhaust 
ports and then complete the three views of the cylinder and steam-chest, with covers, 



50 SENIOR COURSE. 

stuffing-boxes, glands, and bolts. Draw in the slide valve so that its upper edge is 
•^y below the edge of the steam port. This is called the lead of the valve and is the 
amount of opening for admission of steam at the moment the piston is commencing its 
stroke. 

As will be explained later, when the valve is in this position the centre of the 
eccentric is on a radial line passing through the centre of the crank-shaft and making 
an angle with the horizontal plane of the axis of the shaft, which is called the angle 
of advance of the eccentric. Locate this eccentric-centre in the front-view. A line 
drawn from this to the centre of the valve-stem pin will be the centre-line on which 
the eccentric and rod are to be drawn. Project these to the side-view, and then draw 
the connecting-rod, fly-wheel, oil-cups, and all details complete. 

Portions of the steam and exhaust pipes and the arrangement of the drip pipes 
should be drawn, although not shown on the plates. 

After the completion of all the drawings, the student can exercise his inventive 
faculties by making modifications of it. For instance, the Frame can be altered in 
various ways to suit special requirements or different tastes, a disc-crank and outside 
bearing can be substituted, taper shoes can be added to the crosshead for taking up 
wear, the valve can be moved closer to the bore of the cylinder to reduce the clearance 
spaces and consequent waste of steam, by introducing a rocker-arm between the 
eccentric-rod and valve stem with the rock-shaft in a bearing bolted to the side of the 
frame, and many changes can be made which would be valuable practice for an 



MECHANICAL DRAWING. 51 

advanced student. An excellent exercise would be to change this vertical engine to a 
horizontal one, retaining the proportions of the principal parts. 



VALVE MOTION. 

PLATE 35. 

Although it is haraly within the scope of the subject of mechanical drawing to 
discuss the valve motion of a steam-engine, it will nevertheless be of advantage to do 
so, as affording a good example of graphical analysis. 

The diagrams on Plate 35 give partial sections of the steam-cylinder, J size, and 
the valve and seat, J size. Below these are shown circles representing the path of the 
crank-pin, J size, and the path of the centre of the eccentric, \ size. 

The relation of the valve-face to the ports in the seat can be understood best 
when the valve is in its central position as shown in Fig. 4, where it will be seen that 
the inner edges of the valve just close the steam ports by being exactly in line with the 
inner edges of the latter, while the outer edges of the valve extend beyond or lap 
over the outer edges of the steam ports 3V'. This is called the outside or steam lap. 
If the inner edges had more than covered the steam-ports, the excess would have been 



52 SENIOR COURSE. 

inside or exhaust lap, and if they had not entirely covered the ports, the deficiency 
would have been negative inside lap. 

The valve being moved by means of the revolution of the eccentric, it is evident 
that when the latter is on its top centre the former will be at the top of its motion, 
and when the latter is on its bottom centre the former will be at the bottom of its 
motion; consequently, when the valve is in its central position, the eccentric-centre 
will have moved half-way between top and bottom, and will be on the line a b at 
right angles to the axis of the cylinder. This central position of the valve is shown 
in Fig. 4, where it will be seen that the steam-ports are closed, that there is no inside 
lap and that there is ^" outside lap on each end. 

The function of lap will be understood after following the movement during one- 
half a revolution of the crank. Starting with the crank on its top centre and the 
piston at the top of its stroke, as shown in Fig. 1, it is evident that the valve must at 
this moment be in a position to permit steam to enter the cylinder above the piston. 
It has already been shown that when the valve is in its central position, it extends 
beyond the port an amount equal to the lap, and that the eccentric is at right angles 
to the axis of the cylinder. Now, in order to move the valve down sufficiently to 
begin opening the port, the eccentric must be rotated through an angle the sine of 
which is proportional to the desired motion. The amount of this motion is equal to 
the lap plus the required amount of opening of the port at this moment. This open- 
ing is called the lead of the valve, and in this instance is fa". Therefore the eccen- 



MECHANICAL DRAWING. 53 

trie must be rotated on the shaft through such an angle as will move the valve -j^-". 
This angle is called the angle of advance of the eccentric, and in this case is 
30°. 

Fig. 1 shows the crank on its top centre, C, the eccentric at E, the piston at the 
point of commencing its down-stroke and the upper steam-port open the amount of 
the lead. The arrow shows the direction of rotation of the crank. The eccentric is 
thus at an angle with the crank equal to 90° plus the angle of advance, laid off in the 
direction of rotation. 

The piston now moves down and turns the crank, while the eccentric, being keyed 
to the crank-shaft, turns with it and draws down the valve, further opening the steam- 
port. -The relative position of the parts when the eccentric has reached the end of its 
throw, is shown in Fig. 2, where the crank has turned through 60° and the valve has 
made its widest opening to the steam-port. From here the valve alters its direction 
and moves upward, reducing the port opening, and then arrives at the position shown 
in Fig. 3, where the steam-port is just closed and the steam shut off from the cylinder. 
This is called the point of cut-off, that is, the point at which the communication 
between the cylinder and boiler is shut and the force exerted upon the piston is due 
alone to the expansion of the steam confined behind it. 

By again examining these three Figs, it will be seen that the port communicating 
with the cylinder-space below the piston has so far been always open, to a greater or 
less extent, to the interior of the valve, and thence, through the exhaust port, to the 



54 SENIOR COURSE. 

atmosphere, so that the exhaust steam which has done its work in the preceding up- 
stroke, has had free exit. 

With the further rotation of the crank, the valve moves upwards to the central 
position shown in Fig. 4, where it is on the point of exhausting the steam above the 
piston and has just closed the exhaust below. This is therefore the final point at which 
the expansion of the steam above the piston is fully utilized, and also the point at 
which the compression of the exhaust steam below the piston commences. 

The remainder of the half-revolution of the crank results iu opening the 
top port to the exhaust and in keeping the bottom port closed during the travel of the 
lap, thus making a period of compression during which the exhaust steam below the 
piston acts as a cushion to overcome the inertia of the moving parts of the engine, and 
is brought up to a pressure approximately equal to that in the boiler by the time the 
valve opens the bottom port to the live steam. When the crank arrives on its bottom 
centre, Fig. 5, the eccentric-centre is diametrically opposite its first position, Fig. 1, 
and the valve has opened the bottom port the amount of the lead, ■£%". The same 
relative movements will then occur during the up-stroke of the piston, the admission, 
expansion, and exhaust of the steam below and the exhaust and compression of that 
above occurring when the crank arrives at positions diametrically opposite those during 
the down-stroke. 



MECHANICAL DRAWING. 55 

BILGRAM VALVE DIAGRAM. 

PLATE 36. 

The inconvenience and tediousness of the preceding tentative method of analyzing 
the valve motion, has induced the invention of several diagrams, by means of 
which the throw of the eccentric and its angular advance and the amount of lap re- 
quired for the valve, in order to produce such an amount of lead, expansion, and com- 
pression as may be desired (within the limitations of the case) can be readily deter- 
mined by graphical means. The simplest of these is the one devised by Mr. Hugo 
Bilgram. 

In order to get a clear comprehension of the Bilgram Valve Diagram, it will be 
advisable to first make a diagram of the actual relative motions of the crosshead, con- 
necting-rod, crank, and eccentric centre. 

For this purpose draw, upon a sheet 21" by 16", the vertical centre-line of the 
engine and intersect it by the horizontal centre-line of the crank-shaft, as shown in 
Fig. 1, Plate 36. About this intersection describe a circle, 8" diameter, scale J, for 
the path of the centre of the crank-pin. Above the bottom of this circle lay off 20", 
the length of the connecting-rod, and above this, 8", the movement of the crosshead, 
which is equivalent to the stroke of the piston. Divide this stroke into 10 equal parts 



56 SENIOR COURSE. 

and subdivide each part. By setting the large dividers to 20", they can be used for 
the connecting-rod and the percentage of the stroke through which the piston has 
traveled can be very closely approximated for any degree of the crank's revolution. 
Now, concentric with the crank-circle, draw another 1\" diameter, double-size, for the 
path of the eccentric-centre. Two different scales are used for convenience and clear- 
ness, half-size for the motions of the crank, connecting-rod and crosshead, because they 
are large, and double-size for the motion of the eccentric-centre because it is small and 
requires accuracy. 

With the crank on its top centre, locate the eccentric-centre, e, at the given angle 
of advance, 30°, with the horizontal centre-line a 6 of the shaft. A perpendicular 
from e to a b will give the amount the valve has moved from its central position, which 
at this point must be equal to the amount of the lap, plus the lead. With a radius 
equal to the lap, -gj", describe a circle about e, and then the distance between this circle 
and a b will be the amount of lead or the opening of the steam port. This circle is 
called the lap-circle, and the distance between it and a b will show the port opening for 
steam, in whatever position the eccentric-centre may be. As there is no lap on the ex- 
haust portion of the valve, both ports are just closed to the exhaust when the valve is 
central or when the eccentric-centre is on a b, hence the perpendicular distance from e 
to a b will always show the port opening for exhaust. 

If now the crank rotates in the direction shown by the arrow, e will recede from 
a b, increasing the opening of the steam-port, until it reaches the vertical centre line, 



MECHANICAL DRAWING. 57 

after which it will advance towards a b, diminishing the steam opening until the lap 
circle touches a b, when the steam will be cut off, e 1 being the position of the eccentric- 
centre at this moment. To find the corresponding position of the crank, lay off e 1 o c 1 
equal toeoc, or 120°. The bottom exhaust port will at this time be open the amount 
of the steam-lap, ^", and will be closed when the eccentric-centre arrives at e 2 and the 
crank at c 2 , e 2 o c 2 being 120°. When the crank is at c 3 , c 4 and c 5 , the eccentric will 
be diametrically opposite e, e l and e 2 and the port opening can be measured from a b as 
before. 

One trial will be sufficient to show the awkwardness of this method, even when 
the throw, angular advance, and lap have been furnished, but its efficiency will be much 
less when these have to be determined. The trouble with this method is that, although 
the crank and eccentric bear a constant relation to each other, yet they both move in 
relation to the horizontal centre-line a b, which is the base-line from which the motion 
of the valve is determined. 

The invention of Mr. Bilgram consisted in making the line of the crank a 
movable base-line and of locating a fixel-point in the path of the eccentric-centre so 
that the distances from this fixed-point to the line of the crank would be, for every 
position of the latter, the same as the distances from the real eccentric-centre, when 
in corresponding positions, to the line a b. This makes only one moving part to 
handle instead of two, and greatly simplifies the operation. 

Now, alongside of the previous drawiug, repeat the circles of the paths of the 



58 SENIOR COURSE. 

crank and eccentric-centres and show the path of the crosshead-pin as before. If the 
fixed-point e, is locate 1 0:1 the eccentric-circle so that a radial line through it makes an 
angle equal to the angle of advance, 30°, to the right of the vertical centre ne, and 
the lap-circle is drawn, as shown in Fig. 2, it is evident that when the crank is on its 
top-centre, the distance from the line of the crank to the lap-circle will be the same 
as the distance from the lap-circle in Fig. 1 to the horizontal centre-line ab at right 
angles to the crank. Also, it is evident that, if the crank be moved through any 
angle, the perpendicular distance from its line in the new position to the fixed-point e, 
will be the same as that from the line a b to the corresponding position of the eccentric- 
centre in Fig. 1 ; because the line of the crank will have had precisely the same mo- 
tion in relation to the fixed-point in the former case as the eccentric-centre had in rela- 
tion to a 6 in the latter case. 

Therefore, draw a radial line making au angle of 30° to the right of the vertical- 
centre line, and about the point e, where it cuts the eccentric-circle (which is the Jixed- 
point), describe the lap-circle of radius equal to the lap, ^". Tangent to the lap- 
circle, draw a diameter, A A', of the crauk-circle, then A will be the position of the 
crank-pin when the top steam-port is on the point of opening and A' its position 
when the bottom steam-port is on the point of opening. Perpendicular to the radial 
line of the fixed-point, draw B B', then B will be the crank-position when the top 
steam-port and bottom exhaust-port are at their widest opening, and B' its position 
when the bottom steam-port and top exhaust-port are at their widest opening. The 



MECHANICAL DRAWING. 59 

amount of the widest steam-opening is measured from the centre to the lap-circle, 
and is equal to the throw of the eccentric, -I", minus the lap ^", and is therefore £%"■. 
The amount of the widest exhaust-opening is equal to the throw, f ". To find the 
port-openings for any position of the crank, it is only necessary to draw a diameter in 
the required position and a perpendicular from this diameter to the fixed-point e, when 
the length of this perpendicular to the lap-circle will be the steam-opening, and that 
to the fixed-point will be the exhaust-opening. 

Now draw a diameter E E tangent to the lap-circle, then E will be the position 
of the crank-pin when the top steam-port is just closed and E' when the bottom one 
is closed, thus fixing the points of cut-off. The exhaust opening at this moment will 
be equal to the radius of the lap-circle.- A diameter, R R', drawn through the fixed- 
point e, gives the positions of the crank when the valve is central and the confined 
steam at one end is about to be released and the exhaust steam at the other end about 
to be compressed. This fixes the points of release and compression. 

We thus have a means of readily locating the crank for the important points of 
the valve's motion and of determining the port-openings for any position of the crank. 
The top-end of the cylinder has been open to steam from the commencement of the 
stroke until the crank arrived at E, where it is cut off and expansion begins. The 
expansion continues to R, where the steam is released on top and compression begins 
in the bottom-end. 

The lap-circle governs the point of admission and the point of cut-off of the 



60 SENIOR COURSE. 

steam, while the fixed-point e, governs the points of commencement of exhaust and 
compression. Hence the lead cannot be altered without changing the cut-off, and a 
change in either of these alters the exhaust and compression. 

The angular motion of the crank is the same for admission, expansion, exhaust, 
and compression, during both the down and up-strokes, but the motion of translation 
of the piston is not the same on account of the action of the connecting-rod. In 
order to investigate this, take i,he length of the rod in the large dividers, place the 
needle-point at E and describe a small arc cutting the path of the crosshead-pin, 
which lias been laid off in decimal parts of the stroke. It will be found that 
the piston has moved down .81 of its stroke when the steam is cut off. Then de- 
scribe a similar arc from E' and it will be found that the piston has moved up only 
.74 of the stroke, showing a difference of 7 per cent, in the up and down strokes at 
the points of cut off, due to the angularity of the connecting-rod. Repeat the opera- 
tion from R and R' and it will b^ found that the points of release and compression 
are at .945 down-stroke and at .922 up-stroke. 

"Without entering into a discussion of the advisability of equalizing the cut-off 
at the expense of equal leads, the utility of the Bilgram Diagram for the purpose 
will now be investigated. 

Repeat (as in Fig. 3) the centre-lines, crank-circle, and eccentric-circle, and the 
path of the crosshead-pin divided decimally. Let it be required to alter the valve- 
motion so that the steam will be cut off at .73 of both strokes. Locate the position 



MECHANICAL DRAWING. 61 

of the crosshead-pin at these points and from them describe arcs (of radius equal to 
connecting-rod), cutting the crank-circle to determine the corresponding positions of 
the crank E and E. Draw the crank-line for the point of admission at top-end, A, 
allowing a small lead, say TTg", which can be closely approximated, although the 
fixed-point is not yet determined. It is now evident that the fixed-point will be on a 
line bisecting the angle formed by the crank-lines A and E. Draw the bisecting- 
line (R C) and it will be found to be at an angle of 34° with the vertical centre-line. 
This will be the new angle of advance to which the eccentric is to be set. About the 
fixed-point describe a circle tangent to the crank-lines E and A, the radius of which 
will be \\". This is the new and increased steam-lap for top-end of valve. About 
the fixed-point describe a circle tangent to the crank-line E', the radius of which will 
be T$g fr . This is the new and diminished steam-lap for bottom-end of valve. The 
angular advance of the eccentric and the steam-laps of the valve have thus been 
changed to cause the cut-off to take place at 73 per cent, of the stroke of piston at 
both ends of the cylinder. This is called equalizing the cut-off. 

A crank-line drawn tangent to the lap-circle for bottom end will give the posi- 
tion, A', of the crank at point of admission, and the length of a perpendicular from 
the fixed-point e, to the vertical centre-line minus the lap ( T ^V) will give the bottom- 
lead, eV'. This shows the effect upon the lead of equalizing the cut-off by making 
the lap at the bottom of the valve different from that at the top. 

To equalize the release and compression, strike the connecting-rod-arc from R 



62 SENIOR COURSE. 

and C and it will be found that one is at .96 down-stroke and the other at .90 up- 
stroke. Lay off .90 down-stroke and .96 up-stroke and find the corresponding crank- 
lines. Then a small circle, described about the fixed-point tangent to these lines, will 
have for its radius the amount of inside or exhaust-lap necessary to be given to the 
lower end of the valve iu order to make the points of release and compression the 
same at both ends of the stroke. 

There is one feature of this diagram which is a little puzzling until some famili- 
arity has been obtained with the use of it, and that is, the identification of the oppo- 
site positions of the crank in relation to the lap-circles, but reference to the Figs, on 
Plate 36 will make this clear. 

It will be noted that the valve as designed from Fig. 3 would give ^" ^ ess port- 
opening at the top-end than originally. In order to overcome this, the eccentric-throw 
would have to be increased and the laps altered accordingly. To understand this, 
and for the purpose of reviewing the whole subject, draw a diagram as in Fig. 4 for 
the designing of a valve-motion for this same engine, which will give \\" top port- 
opening, equalized cut-off at § or .625 stroke, and equalized exhaust and compression. 
From shaft-centre describe an arc of radius equal to the port-opening, locate the crank- 
lines for the points of admission and cut-off for the down-stroke, bisect the angle of 
these crank-lines for the angle-of-advance and find by trial a point on this line from 
which a circle can be drawn tangent to the crank-lines and to the arc which was 
drawn of radius equal to the port-opening. This point will be the fixed-point e, and 



MECHANICAL DRAWING. 



63 



a circle described about the shaft-centre and passing through the fixed-point will bo 
the eccentric-circle. Locate the crank-line for cut-off on up-stroke and draw the 
bottom steam lap-circle. Locate the crank-lines for release and compression and draw 
the bottom exhaust lap-circle. Measure the diagram for the a:igle-of-advance, the 
eccentric-throw, and the valve-laps. The utility of making this part double-size will 
then become apparent, and also a good idea of the possibilities and limitations of the 
plain slide-valve will be obtained. 

There is a slight error in all these diagrams, due to the angularity of the eccentric- 
rod, but in ordinary cases the rod is so long in proportion to the throw of the eccen- 
tric that it is not taken into account. 

The three diagrams give the following proportions, which are arranged symmetri- 
cally for the purpose of comparison : 

Fig. 2. 



Top Steam Lap — ^" '. 

Top Exhaust Lap — 0. 

Movement of Valve— \\" . 

Top lead — -gL". 

Cut-off at .813 down-stroke. 

Compression at .945 down-stroke. 

Release at .915 down-stroke. 



Bottom Steam Lap — 3V'. 
Bottom Exhaust Lap — 0. 
Angular advance — 30°. 
Bottom lead— jL". 
Cut-off at .742 up-stroke. 
Compression at .922 up-stroke. 
Release at .922 up-stroke. 



64 



SENIOR COURSE. 



Fig. 3. 



.11" 

l 4l • 



Top Steam Lap— Q". 

Top Exhaust Lap — 0. 

Movement of Valv< 

Top Iead-^". 

Cut-otf at .734 down-stroke. 

Compression at .898 down-stroke. 

Release at .961 down-stroke. 



Bottom Steam Lap — 1%\". 
Bottom Exhaust Lap — tV. 
Angular Advance — 34°. 
Bottom lead— A". 

6 4 

Cut-off at .734 up-stroke. 
Compression at .898 up-stroke. 
Release at .961 up-stroke. 



Fig. 4. 



.115" 
x 16 ' 



Top Steam Lap — ■££?". 

Top Exhaust Lap — 0. 

Movement of Valve- 

Top lead— J ¥ ". 

Cut-off at .625 down-stroke. 

Compression at .838 down-stroke. 

Release at .9 down-stroke. 



Bottom Steam Lap — &>?"• 
Bottom Exhaust Lap — g 9 ¥ ". 
Angular Advance — 41°. 
Bottom lead — &". 
Cut-off at .625 up-stroke. 
Compression at .838 up-stroke. 
Release at .9 up-stroke. 



MECHANICAL DRAWING. 65 

ADJUSTABLE CONNECTING ROD AND ECCENTRIC 

ROD. 

PLATE 37. 

The Connecting-Rod and Eccentric-Rod already drawn for the 6" by 8" Engine 
possess the merit of simple construction but lack conveniences for taking up wear. 
Other types, which have such conveniences, are shown on Plate 37. 

The crank-end of the connecting-rod is made rectangular and to it is fitted a 
wrought-iron strap which embraces the brass box (in halves) for the crank-pin. The 
strap is held in place by a gib and key, which pass through a slot, the gib bearing 
against one end of the slot in the strap and the key bearing against the other end of 
the slot in the roil. As the adjoining edges of gib and key are tapering, an adjust- 
ment of the strap on the rod can be obtained for the purpose of determining the 
distance apart of the two half-boxes and of drawing them together as they wear. A 
set-screw holds the key in the desired position. 

The other end of the connecting-rod has a rectangular opening through it, into 
which are fitted two half-boxes for the crosshead-pin, a block, and a wedge, all of 
brass. The end box is put through from the front, there being no flanges on top and 
bottom at back, and is slipped to the end and kept in position by the end flanges. 



66 SENIOR COURSE. 

The next box is then put through from the front. It has flanges on top and bottom 
of front only. The block is put through from the back. It has flanges on top and 
bottom of back only and has a vertical tongue which fits a groove in the adjoining 
box. The wedge fills up the remaining space and serves to adjust the distance apart 
of the boxes. 

The eccentric-rod has a similar rectangular end and hole through it, but it has 
only the half-boxes without flanges, and the wedge, the forked end of the valve-stem 
being depended on to keep the parts in place side-ways. 



BRASS GLOBE VALVE. 

PLATE 38. 

This is a drawing to a scale of 4" to the foot, or J size, of a 1 J" Stop Valve for 
the steam-pipe of the 6" by 8" Engine. All the parts are brass, except the hand- 
wheel, which is cast-iron. 

The valve-seat is in a circular plate, ^" thick, concentric with the vertical axis, 
and in the plane of the horizontal axis of the spherical shell. The seat is conical, the 
angle of the cone being 90°, or 45° on each side, and extends half through the plate, 



MECHANICAL DRAWING. 67 

the remainder of the opening being cylindrical, 1|" diameter. This circular plate is 
held in the centre of the globe by two cylindrical plates, one up and on the outlet 
side, and the other down and on the inlet side, each extending far enough around to 
meet a diagonal plate across the globe. By this means, if the opening in the plate is 
closed, the communication between the inlet and outlet is shut off. This closure is 
produced by the valve which fits the conical seat. The stem has a spherical end bear- 
ing against the interior of the valve to permit the latter to adjust itself to the seat. 
A gland is screwed into the valve for the collar on the stem to bear against when 
lifting. The stem has a square thread, 4 per inch, fitting a nut which is screwed into 
a cylindical projection on the globe. This nut has an extension to afford a stuffing- 
box for preventing leakage of steam. The stuffing-box has a washer at the bottom to 
act as a seat for the packing and a gland and nut at the top to compress it. The inlet 
and outlet of the globe are tapped for \\" pipe. 



TOOTHED GEARING. 

The transmission of motion from one shaft to another, which is parallel to it, is 
very largely accomplished by means of gear-wheels, which are cylinders with teeth 
upon their circumferences. In a pair of wheels the teeth of one engage with those of 



g8 SENIOR COURSE. 

the other so that the rotation of the one compels that of the other. It is very import- 
ant that the relative velocities of the two wheels should be uuiform, and that the 
transmission of the force from one to the other should be smooth and free from blows, 
and that the sliding of the teeth should cause as little loss from friction as possible. 
All these desirable qualities depend upon the nature and accuracy of the form given 
to the teeth. 

In Fig. X let o o' be a portion of a line joining the centres of two cylinders A and 
B, arcs of whose circumferences are shown by P P, P' P' , touching each other at p, and 
let the diameter of cylinder B be one-fourth that of A. If the friction between these 
cylinders be sufficient to prevent slip, every movement of the circumference of A will 
cause an exactly similar movement of the circumference of B. Tins would be the 
perfection of transmission as regards uniformity of motion and absence of shock. 
The length of the circumference of A would move the same length of circumference 
of B at the same velocity and with perfect smoothness. As A is one-fourth the 
diameter of B, its circumference is one-fourth the length of that of B, and 
it would make four turns to one of B. This is called the angular velocity 
ratio and if there is no slip or irregularities of any kind between the circumferences, 
the ratio is said to be constant. The want of sufficient friction between the 
surfaces, compels the use of teeth, and the problem is to so shape these teeth that 
they will transmit the required motion and force from one wheel to the other with a 
constant velocity ratio. 



MECHANICAL DRAWING. 



69 







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TV 


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7/1 \/ 




c 






^""t^ 










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____^-^a 


i \ \ 

5 \ \ 


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Now reduce the diameters of these cylin- 
ders proportionately — that is, so that one 
shall still be four times that of the other, as 
shown by 6 b, b' b' . Wrap an inelastic cord 
around 6 b in the direction shown by the 
arrow, and then pass it down between the 
two and around b' b' in the opposite direc- 
tion. Then the cord will leave the first 
cylinder at t and join the second at t' , and 
will cross the line of centres, o o', at the 
original point of contact p. If either cylin- 
der be now rotated it is clear that the cord 
will transmit the motion to the other cylinder 
at the same constant velocity ratio as origi- 
nally. If a marking-point be fixed to this 
cord and the cylinders be rotated, the move- 
ment of the cord in passing from one cylinder 
to the other would cause the marking-point to 
trace an involute to each cylinder on a plane 
perpendicular to the axes, hence, if these 
two involute curves be used for the shape of 



70 SENIOR COURSE. 

# 

the teeth in the corresponding wheels, such teeth must produce a coustant velocity- 
ratio. 

Referring to Fig. X, radii drawn from the centres of the wheels, perpendicular to 
the cord t t' , will touch the Avheels at t and t' , the points of tangency of the cord. 
Suppose the marking-point to be at t and the wheel A to turn in the direction shown, 
then the point will travel along tt' , tracing an involute from the circle bb, called the 
base-circle of A, and at the same time tracing another involute toward the circle b' b' , 
called the base-circle of B. Several positions which would be occupied by this one 
pair of involutes during the movement are shown by the figure. They touch each 
other only on the line tt', which is, therefore, called the path of contact or line of action, 
and which is normal to the curves iu all positions, and which always passes through 
the point p, where the original friction cylinders touch each other. These cylinders, 
P P, P' P', are called the pitch circles, because the pitch of the teeth or the length of the 
arcs of these circles included between the side of one tooth and the same side of the 
next, is measured upon them. The point p is the pitch-point where the teeth touch 
each other on the line of centres. 

The pitch is an arc of the pitch-circle which includes a tooth and a space. The 
tooth acts as a cantilever in transmitting the force from one wheel to the other, and 
its strength is dependent upon its form, its dimensions, and the material. By what- 
ever system the form is produced it will vary with the radius of the wheel, the root 
of the tooth becoming smaller and consequently weaker as this radius diminishes. 



CIIANICAL, DRAWING. 



71 



ivx.: . 










"^O 


77 / 




v\ l/A 






b^^/ A 

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<f]\ \l 


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\ V 



The thickness of the tooth on. the pitch-Hue 
is necessarily one-half the pitch, less a suffi- 
cient amount to allow clearance in the ad- 
joining space for the tooth of the other 
wheel. The distance which the tooth ex- 
tends beyond the pitch-circle is called the 
addendum. It is that portion of a radius of 
tjie wheel included between the circles P and 
a or I s " and a'. It determines the length of 
the cantilever, and should bear a fixed ratio 
to the pitch to insure interchangeability, uni- 
formity, and convenience of manufacture. 

The portion of the involute outside of the 
pitch-line constitutes what is called the face 
of the tooth, while that inside the pitch-line 
is the flank. 

The selection of the best form for the 
tooth and proportion for the addendum has 
been subject for dispute from the time of 
Camos, who first scientifically investigated 
the subject in 1752, to the present day, but 



72 SENIOR COURSE. 

the author is convinced that the involute form with an addendum equal to three- 
tenths of the pitch, and with the smallest number of teeth in any wheel limited to 
twelve, is superior to any other system. 

In Fig. X, let the circumference of the pitch-circle, P P, be divided into twelve 
equal parts for the pitch, and the radius of the addendum-circle, a a, be made larger 
than that of the pitch-circle by an amount equal to .3 pitch. As one tooth touches 
the other only upon the path of contact, t V, it is evident that the action will com- 
mence at c, where a' a' cuts t V, and will end at c', where a a cuts it. If the diameter 
of a a were increased, c' would move further away from p and more of the involute 
of B would be brought into action. The distance, p c! , would reach its maximum 
when A became a rack or wheel of infinite size. So, in the case of B, an increase in 
the diameter, of a' a' (A remaining as in the Fig.) would move c from p until a' a' 
arrived at s s, which would be the addendum-line of a rack, and the involutes would 
commence action at t, and end at c! '. Hence the line of action of the smallest wheel 
(12 teeth), gearing into a rack, must pass through the pitch-point, p, and be tangent 
to the base-circle, b b, at the point where the addend um-liue, s s, of a rack cuts it. To 
find this point, t, use the triangle, moving it so that one side of its right-angle is in 
contact with p, and the other with o, until the corner touches the line s s, and draw o t, 
1 1'. The angle, t, o, p, will be found to be about 23°. Calculation shows it to be 23° 
21', but as the difference will be practically inappreciable, take 23° as the standard 
angle. The base circles being drawn tangent to the line of action, their radii will be 



MECIIAKICAL DRAWING. 



73 





Tvo.X. 










x n 






1 




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v\ 








1 ^^ 


1 










1 


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•proportional to cosine 23° or .92 radius of 
pitch-circle, and p t and p t' will be pro- 
portional to sine 23° or .39 radius of pitch- 
circle. Hence, to draw this line of action, 
describe an arc of radius equal to .92 pitch 
radius from the centre of the wheel and in- 
tersect it by an arc of radius equal to .39 
pitch radius from the pitch point. 

The line of centres divides the path of 
contact into two parts, c p andp c', and the 
arc of the pitch-circles which is equivalent 
to the movement of the point of contact 
from c to p, is called the arc of approach, 
while that equivalent to the movement from 
p to c' is called the arc of recess. The sum 
of these must always be greater than, the 
pitch. Perpendiculars to the line of action, 
drawn from the points of tangency, t and t' , 
to the pitch-circles, will include the angle of 
action. 

The thrust of the teeth of the wheel A, 



74 SENIOR COURSE. 

upon those of B, is in the direction of tine line of action, tt'. This is called the 
obliquity of action of the teeth, and the fear of its producing excessive friction in the 
journals of the wheels has hitherto prevented the adoption of a sensible and correct 
system of involute gearing. This fear has been induced by the statement, to be found 
in most works on the subject, that the angle of obliquity should not exceed 15°. 
With this angle, the number of teeth in the smallest wheel, which will act properly 
with those in a rack, becomes so great as to render the system useless, unless the faces 
of the teeth of the large wheels and racks are rounded off to prevent their inter- 
ference with the flanks of the small wheels, a device which destrovs much of the 
wearing surface and diminishes the length of the path of contact. 

Increasing the angle of obliquity to 23° does not affect the efficiency of the gear- 
ing, except that it adds a trifling amount to the pressure on the journals, but this side- 
thrust is constant and steady, and not pulsating, as will be seen farther on to be the 
case with cycloidal teeth, and the obliquity is actually less than it is at the beginning 
and end of the arc of action of the latter. 



MECHANICAL DRAWING. 75 

INVOLUTE GEAR TEETH. 

PLATE 39. 

In order to get a clear understanding of the involute form of teeth, it will he well 
to now make a full-size drawing of the two extreme cases, a pinion of 12 teeth gearing 
into a rack and into a similar pinion, and also into a wheel of intermediate size, say of 
32 teeth.. The pitch should be made as large as the drawing facilities will permit. 
If the standard sheet, 16" by 21", is used, the pitch should be 2|", as shown in the 
Plate. 

The pitch being the length of an arc of the pitch-circle included between the side 
of one tooth and the same side of the next, the pitch-circle will be made up of as many 
of these arcs as there are teeth ; and its circumference will be equal to the product of 
the pitch by the number of teeth. The ratio of the diameter of a circle to its circum- 
ference being 3.1416, if we divide the former product by this number we will obtain 
the diameter of the pitch-circle, called the pitch-diameter. The addendum being .3 
pitch, twice this, or .6 pitch, added to the pitch-diameter, will give the outside-diameter 
of the wheel, The depth of the space, below the pitch-line should be made from .35 
pitch to .4 pitch. As we are only considering accurately-made teeth, the former 
amount will be sufficient, and .7 pitch subtracted from the pitch-diameter will give the 
inside or root-diameter. 



76 SENIOR COURSE. 



If p=pltch, n=number of teeth, P=pitch-diarneter, O=outsiae diameter, B= 
root-diameter, and ^=3.1416, then. 

P='- v— - n=— 

x tt> V — n > U — p • 

0=P+.6p. B=P— .7p. 

For 12 teeth, 2J" pitch, P= 2 3 5 ^ 2 =9.549", O=9.549" + 1.5"=11.049", and 
B=9.549"— 1.75"=7.799". 

For 32 teeth, 2J" pitch, P= 2 3 5 ^| 2 =25.465 / ', 0=25.465" + 1.5"=26.965", and 
B=25.465"— 1.75"=23.715". 

With these dimensions, draw the pitch-circles, outside circles, and root circles of 
the pinions and wheel, and, below the pinion, draw the pitch-line, outside liue, and 
root line for the rack-teeth. 

If facilities are not at hand for measuring hundredths of an inch, use the Table 
of Decimal Equivalents, on page 96, to find the nearest sixty-fourth. For instance, 
the pitch diameter of the 32-tooth wheel is 25. 465". This will be found by the Table 
to be .003" ess than 25g2". 

Next draw the line of action and its normals (shown by heavy lines on the Plate), 
at angles of 67° and 23°, respectively, with the line of centres, and draw the base- 
circles tangent to the line of action. The pitch-point divides this line into two por- 
tions, the upper belonging to the pinion and the lower to the wheel. Each portion 
represents a flexible, inelastic cord, wound upon its respective base-circle. If the ex- 
tremities of the two portions of the cord (represented by the pitch-point) be swung 



MECHANICAL DRAAVING. 77 

in and out from the base-circles they will describe involutes which, as we have seen, 
will be correct shapes for the teeth of these wheels. 

To plat these involutes, divide the line between the pitch-point and point of 
tangeucy into any number, say three, equal parts, and step off these distances on the 
base-circles as many times as will be necessary to produce enough involute for the 
tooth. The three steps taken on the base-circle from the point of tangency, reaching 
beyond the line of centres, measures where the end of the cord will be when swung in 
to the base-circle and is the point of origin of the involute. Draw tangents to the 
base-circle at each of the stepped points, and upon each tangent step the same number 
of spaces as its point of tangency is from the point of origin. A curve passed through 
the final points will be the involute required. 

The involute for a tooth of any pitch and for a wheel of any size can be very 
closely approximated by two circular arcs having their centres on the line of action, 
one arc extending from the pitch-circle out and the other from the pitch- circle in. The 
length of the radii of these arcs for any number of teeth can be obtained by multiply- 
ing the constants given in the Table on page 100, opposite the required number of 
teeth, by the pitch in inches. In the present case, the radius of face of the 12-tooth 
pinion will be .950 multiplied by 2-J, or 2.375", and the radius of flank will be 
.668x2J=1.67 // . Describe the face-arc from the pitch-circle to the addendum-circle, 
and the flank-arc from the pitch-circle to the base-circle, keeping the centre from 
which each radius is struck always on the line of action. The flank from the base- 



78 SENIOR COURSE. 

circle to the bottom of the space is a radial Hue. In order to strengthen the root of 
the tooth, a fillet is made in the corner. This is an arc of a circle tangent to the flank 
and to the root-circle, and on small wheels should be as large as can be made to clear 
the engaging tooth. The Table gives the maximum radii of these fillets for \" pitch 
for any number of teeth. For any other pitch, multiply the figure in the Table by 
the given pitch in inches. The radius for this 12-t. pinion will be .15x2J=.375" or 

3// 

8 • 

In obtaining the radii for face and flank of the 32-t. wheel, it will be found that 
the nearest exact figures are for 33 teeth, helice the differences for one tooth, given at 
the foot of the Table, must be subtracted from the figures given for 33 teeth; thus, 
radius of face=(2.413—.07)x2|=5.858", and radius of flank=(1.613— .045)x2i= 
3.920". Make small circles around the centres on the line of action, from which the 
face and flank are struck, to facilitate finding them later on. 

Now step the pitch around the pitch-circles, using a spring bow dividers with 
screw adjustment, in order to be able to gauge the alteration which trial may show to 
be necessary. Then mark the thickness of the teeth on the pitch-line, making it less 
than half the pitch to give side clearance in the space. This clearance is usually 
made .02 pitch for cut teeth, and .05 pitch for cast teeth, which makes the tooth and 
space respectively .49 and .51 pitch for cut teeth, and .475 and .525 pitch for cast 
teeth. 

Having now spaced the teeth, describe circles from the centres of the wheels, pas- 



MECHANICAL, DRAWING. 79 

sing through the centres from which the faces and flanks of one tooth have already 
been described, for the loci of the centres for the faces and flunks of all the other 
teeth. 

The Rack, being a wheel of infinite size, its corresponding involute will be a 
straight line perpendicular to the line of action, therefore step off the 2J" pitch and 
mark the thickness of the teeth on the pitch-line and, through these marks, draw 
straight lines making an angle of 23° in opposite directions for the faces and flanks 
of the teeth. 

After completing all the teeth in the wheels, draw lines of action making the 
same angle, 23°, in the opposite direction from the former ones, in order to see the 
path of action if the wheels turned in the opposite direction. 

Involute teeth in which the angle of action is other than 23° can be drawn in the 
same manner, by making the line of action at the required angle, drawing the base- 
circles tangent to it, and generating the involutes from these base-circles, if such teeth 
are required to meet prejudices which have been handed down, or to maintain systems 
already adopted, but care must be taken that the addendum-line of the wheel never 
intersects the base-circle of the pinion beyond the point of tangency of the line of 
action, as in this case there will be interference between the faces of the teeth of the 
wheel and the flanks of those of the pinion. To demonstrate this, draw a 
pinion with 12 teeth, gearing into a rack, with the angle of action 1G°, the limit 
which has usually been assigned to it. Make a tracing of the rack and roll it upon 



80 SENIOR COURSE. 

the pinion, keeping the pitch-lines tangent, and this interference can be seen. With 
an angle of 15°, the wheel cannot have less than 30 teeth to gear correctly with the 
rack. This fact destroys the usefulness of the 15° system, and the assertion that the 
angle should not exceed 15° has consequently prevented any general use of this shape 
of teeth. 

The statement that an obliquity of action exceeding 15° produces an injurious 
amount of journal friction is an exaggeration, and no fear need be had of using 23° 
as here recommended. On the contrary, the teeth made on this system will be stronger, 
will run more quietly, and be more satisfactory in every respect than any other kind. 

The greatest reason for the superiority of involute teeth is that they will work 
together equally well if the pitch-lines are not tangent to each other ; that is, the 
centres of the wheels can be separated a little or be brought closer together without 
affecting the correct action of the teeth. For instance, if the centres of the pinion 
and wheel of Plate 39 were each moved ■£$", one to the right and the other to the left, 
the base-circles would remain the same in diameter, the pitch-point would stay at the 
same relative distances from the wheel centres, the pitch-diameters and angle of action 
would be slightly increased and the addenda decreased, but the velocity-ratio would 
remain constant and the same as it was before. 

This is a very valuable property of involute teeth because it eliminates the bad 
effects of several errors which are very liable to occur in constructing gearing • namely, 
the obtaining of accurate diameters for the wheels, the production of cutters which 



MECHANICAL DRAWING. 81 

are correct in relrtion to the pitch-line, and the cutting of the spaces to the proper 
depth to bring the point of the curve intended to be at the pitch-line, precisely at it. 
In addition to these an error is apt to occur in boring the bearings for the journals of 
the wheels, by not getting them at exactly the correct distance apart. 



APPROXIMATE INVOLUTE TEETH. 
PLATE 40. 

In drawing the preceding Plate, the exact involutes for one pair of teeth were 
first generated and the rest of the curves made by circular arcs of the radii given, 
when it was seen that there was scarcely a perceptible difference between the 
two. Practically, the error arising from the use of these arcs is less than would occur 
in attempting to make cutters of absolutely correct shape, except by means of a 
machine which would automatically generate the curves and form the cutters to 
them. 

For the purpose of getting familiar with the use of the Table on page 100, and 
of seeing the shapes of teeth made on this system, make a full-size drawing showing 
a few teeth each in wheels having 12, 20, 27, 33, and 42 teeth of 2 J" pitch. Draw 
the line of centres and the pitch-circles, and through each pitch-point draw the line of 



82 SENIOR COURSE. 

action, making an angle of 67° (the complement of 23°), with the line of centres. 
Find from the Table, the radii of the flanks and faces for the several different numbers of 
teeth, and multiply them by the pitch, 2J", for the radii required. Strike the arcs 
from the pitch-point outward, for the faces, and inward for the flanks, keeping the 
centres always on the line of action. Lay off the pitches and thickness of teeth on 
the pitch-lines. From the centres of the wheels, describe circles passing through 
the centres on the lines of action from which the arcs were struck, and upon these 
circles take the centres for the arcs of all the other teeth in each wheel. This will be 
found a convenient, quick, and remarkably close approximation to the true involutes. 

Of course, if any other angle of action than 23° is used, the figures in the Table 
will not apply. 

It will be noted that these figures are not given for all numbers of teeth beyond 
18. This is done to enable a complete set of wheels to be cut by a limited number of 
cutters, without any very serious error arising therefrom. Prof. Willis first suggested 
this, and proportioned the intervals so that the error, between the smallest and largest 
number of teeth in each interval would be the same. For instance, if a wheel with 
49 or 72 teeth is made with a cutter of the proper shape for 58 teeth, the error will be 
the same as in a wheel with 37 or 48 teeth made with a cutter proper for 42. 

If the exact radii for any of the intermediate numbers are required, they can 
be readily obtained by the use of the differences given at the foot of the Table. The 
radius of the face for \" pitch increases .07" for each tooth, and of the flank .045". 



MECHANICAL DRAWING. 83 

The locus of the centres of the radii of the faces is a straight line, as is also 
that of the flanks, but these lines are neither parallel to each other nor perpendicular 
to the lines of action. 

By means of the following formulae, in which R=radius of pitch-circle, the 
radii for teeth of 1" pitch can be obtained, when the angle of obliquity is 23°. 

Eadius of Face=.175 (R+0.66"). 
Radius of Flank=. 113 (R + l. 14"). 



DIAMETRAL PITCH. 

PLATE 41. 

As the length of the circumference of the pitch-circle of a gear-wheel is the pro- 
duct of the pitch by the number of teeth, and as the ratio of this circumference to its 
diameter is 3.1416, it follows that if the pitch is an even measurement, the diameter 
will be decimal, and if the diameter is made even the pitch will become decimal. It 
also follows that the number of teeth is proportional to the diameter. If a wheel 5" 
pitch diameter has 20 teeth, one of 10" will have 40 teeth, and they will each 



84 SENIOR COURSE. 

have 4 teeth for every inch of diameter, while the circumferential pitch will be A"I5 
or .7854" 

This method of indicating the pitch, by specifying the number of teeth per inch 
of diameter, is often a convenience in making calculations, and in enabling the distance 
between the centres of the wheels to be made to coincide with the system of measure- 
ments in common use. The pitch is expressed as thus : 4 per inch, or No. 4 pitch. 
The Table on page 99 contains a column of diametral pitches with the corresponding 
actual pitches, arranged in proper order in relation to the usual pitches which contain 
vulgar fractions. It also gives the addendum outside and the depth inside the pitch- 
line, the former being .3 pitch and the latter .35*pitch. 

A system is largely used in which the addendum is made equal to 

•vr 1 i = — i — t^t-- For instance, the addendum for No. 4 pitch is \". for 

No. of teeth per inch of diarn. 

No. 8 pitch, |", and so on. This makes the addendum equal to £ p, or .3173 pitch, 
which would necessitate an increase of the angle of action to 24°. 

The advantage of using exclusively the diametral-pitch system has been very 
much overrated, for unless it is restricted to 16,8,4,2 and 1 per inch, the vulgar 
fractious become troublesome and liable to cause mistakes in the shop, while its con- 
venience is not much greater than that of the Table on Page 99, The fifth column 
in that Table gives figures which, multiplied by any given number of teeth of any 
pitch, will give the required pitch diameter, to which is to be added twice the adden- 



MECHANICAL DRAWING. 85 

dum, and from which is to be subtracted twice the depth (as found on the same 
horizontal line) for the outside and root diameters respectively. 

The fear of decimal measurements for shop use is unfounded, because, with a 
little experience, they can be as conveniently and accurately made as the ordinary 
ones. It is much better to accept the decimals unconditionally, than to devise incor- 
rect or mongrel systems of gearing in order to avoid them. 



PROPORTIONS OF GEAR WHEELS. 

Plate 41 is to be drawn as an example of an arm-wheel, a plate-wheel, and a 
pinion, in order to become acquainted with a good conventional method of showing 
them, with the proportions to be given to the various parts, and with diametral pitch. 

Draw the centre-lines, the pitch-circles, the outside-circles, and the root-circles 
for 80, 49, and 12 teeth, 8 per inch. Make the width of face of the wheels, in the 
top-view, from 2 to 2J times the pitch or, in this case, 1". Make the top-view in 
section, presuming that the section does not cut the teeth, and show the pitch-lines and 
tops and bottoms of teeth as in the Plate. This is easier and very much clearer than 
attempting to find where the central plane would cut a tooth. In the front-view, 
make the pitch-circles blue, the root-circles dotted, and the outside-circles full, except 



86 SENIOR COURSE. 

where they run together. Make the thickness of the rim below the bottoms of the 
teeth equal to about f the pitch, and the depth of the web below this about equal to the 
pitch, if the wheel has arms. Make the widlh of the arms at the web from 1|- to 2 
times the pitch, according to the number of teeth, say 1J times for 25 teeth, and 2 
times for 100 teeth. Taper the width of the arms from \\" to \" per foot of length, 
and make their thickness equal to .4 their width. The thickness of the web is the 
same as that of the arms which join it. In plate-wheels, make the thickness of the 
plate about .6 pitch. Make the diameter of the hub from If to 2 times the diameter 
of the shaft, and the length of the hub not less than 1 \ times the diameter of the 
shaft. 

Make this drawing full-size, marking the dimensions as shown, and giving the 
tooth-data in columns, apart from the lines of the drawing, for the sake of clearness. 



CYCLOIDAL GEAR TEETH. 

PLATE 42. 

Although involute teeth, properly designed and constructed, possess decided 
practical advantages over the cycloidal, the action of the latter is perfect if their form 
and the coincidence of their pitch-lines are perfect. An understanding of this 



MECHANICAL DRAWING. 87 

form of tooth is, therefore, important, particularly as it is in more general use than 
the other. 

If a circle is rolled on a straight line, a point on its circumference will trace a 
curve, which is called a cycloid. If rolled on the outside of another circle, the curve 
generated is called an epicycloid, and if rolled on the inside, it is called a hypocycloid. 

Draw the pitch-lines of a piuion of 12 teeth gearing into a rack and also into a 
wheel of 32 teeth, 1\" pitch, as shown in Plate 42. Draw the rolling-circles, of 
diameter equal to half that of the pinion, tangent to the pitch-circles, and to each 
other at the pitch-point. Imagiue the wheels and rolling-circles to revolve about their 
fixed centres with a uniform velocity-ratio. Take the pitch-point as the marking 
point of the rolling-circle on the outside of the pinion and the inside of the wheel. 
This marking point will move along the circumference of the rolling-circle and, in 
doing so, will trace an epicycloid from the pitch-circle of the piuion outward, and a 
hypocycloid from that of the wheel inward. As these two curves are both generated 
by the same point, at the same time, they must be tangent to each other at every posi- 
tion in the path of the point, and as the velocity-ratio of all the circles is constant, 
that produced by the action of the two curves upon each other must also be constant. 
If this is true in one case, it is in all, and curves generated by this means are proper 
forms for the teeth of wheels. 

As regards the correct action of the teeth of any individual pair of wheels, the 
diameter of the rolling-circles is a matter of indifference, provided the same circle is 



88 SENIOR COURSE. . 

used to generate the faces of the teeth of one wheel aud the flanks of the other, but 
as interchangeability is desirable and essential, it is necessary that the same rolling- 
circle be used for all wheels whose teeth are of the same pitch. 

If the rolling-circle is one-half the diameter of the wheel inside of which it 
rolls, the hypocycloid generated thereby will be a radial line. Experience has shown 
that the flanks of the teeth should never be made thinner than would be produced by 
radial lines; therefore, if a pinion with 12 teeth be taken as the smallest allowable 
wheel, a rolling-circle of half its diameter will make the flanks of its teeth radial and 
will be the proper one to use for all wheels of its pitch. 

To describe the curves, set the spring bow dividers to any distance, say \ pitch, 
and step this distance on the pitch-lines. Draw the paths of the centres of the rolling- 
circles, and draw normals to the pitch-lines from the stepped points, to intersect these 
paths. Strike arcs of the rolling-circles from the points thus found, and step back on 
each arc the distance from the pitch-point to the point of tangency of the arc with 
the pitch-circle, being careful that the original distance taken in the dividers has not 
been changed. Curves passed through the final-points will give the shape required. 
Then draw the outside and root-circles and mark off the pitch and thickness of teeth 
upon the pitch-lines. Use .3 pitch for the addendum and .35 pitch for depth as 
before. 

To avoid the difficulty of repeating the cycloidal-curves for every tooth, find 
centres from which to strike circular arcs to approximate these curves and draw the 



MECHANICAL DRAWING. 89 

loci of these centres, from which the arcs of all the teeth can be quickly struck. 
Circular arcs will not approximate very closely to the true curves, but the accuracy is 
sufficient for purposes of drawing, and is much greater than is attained in teeth shaped 
by any "rule of thumb.'' Many systems have been devised for finding centres and 
radii for these arcs, the one in most general use being Professor Willis' Odontograph. 
Professor Reuleaux's graphical method is also very good. The closest approximation, 
however, is obtained by constructing the cyeloidal-curves for the several numbers of 
teeth of large pitch, and determining graphically the centres and radii of arcs to pass 
through three (the central and two extreme) points of the working-part of the curves. 

The figures for cycloidal teeth in the Table on page 100 have been found in this 
manner, and from it can be obtained the distance inside of the pitch-line for the line 
of centres for the faces, and the distance outside of the pitch-line for the line of centres 
for the flanks, and also the radii of the faces and flanks, by multiplying the corres- 
ponding figures in the Table by the pitch in inches. 

These arcs are flatter near the pitch-point and fuller near the addendum and 
root-points than the true curves, particularly for small numbers of toeth, and are not 
as close an approximation as those for involute teeth, while the nature of the former 
requires greater accuracy than that of the latter. 

After completing this drawing (Plate 42) of cycloidal teeth, it will be seen that 
the path of contact, which comprises arcs of the opposite rolling-circles included 
within the tsvo opposite addendum-lines, shown by heavy lines in the Plate, isinflexi- 



90 SENIOR COURSE. 

ble, requiring exact coincidence of the pitch-lines and exact relation between the 
curves, radially, which is very difficult to attain. It will also be seen that the ob- 
liquity of action at the commancement and end of the path is as great as in the 23° 
involute. The weight of evidence, both from experience and analysis, is getting on 
the side of involute teeth, and it would be very desirable if the best possible system 
could be established and universally adopted. 



BEVEL GEARS. 

PLATE 43. 

The cylindrical wheels, which have so far been considered, can be used for trans- 
mitting motion from one shaft to another, only when these shafts are parallel. 

If the axes intersect, the pitch-surfaces must be cones instead of cylinders, the 
apices of the cones being at the point of intersection. Wheels having conical pitch- 
surfaces are called bevel wheels. The usual case is where the axes are at right angles, 
although the principle is the same in all cases. 

The pitch-cones are sectors of a sphere, their axes intersect at the centre of the 
sphere, and their lines of taugency are elements of their surfaces, which all meet at the 



MECHANICAL DRAWING. 91 

intersection of their axes. Their velocity-ratio is independent of the diameter of the 
imaginary sphere ; that is to say, if the sphere is enlarged and the angles of the cones 
remain the same, the velocity-ratio will remain the same, because the diameters of the 
sectors will increase proportionately. These diameters are the pitch-diameters of the 
bevel wheels, and are calculated in the same way as for cylindrical wheels, so that the 
pitch-circles of bevel wheels are the circles of the sphere formed by the sectors 
or pitch-cones. If the pitch aud thickness of the teeth be laid off on these circles, 
each pitch-point wi-U be the extremity of an element of the conical surfaces, which all 
converge to the centre of the sphere. To produce bevel gears from these pitch-cones 
involves the same principles as have been investigated for the production of spur- 
wheels from their pitch-cylinders, but the operation becomes very jmueh complicated, 
theoretically, from the fact that the rolling of the generating line for describing the 
teeth should be done upon conical surfaces instead of cylindrical. If, for instance, 
tie teeth are to be cycloidal, their shapes should be generated by rolling a sector on 
the outside of oue pitch-cone aud on the inside of the other and vice versa, when the 
element of the surface of the rolling sector, which coincided with the pitch-point at 
the start, would generate cycloidal teeth, every element of which would converge to 
the centre of the sphere, the shape of the teeth appearing on the surface of the sphere, 
where their size would be the greatest, from whence it would diminish to a point at 
the centre. 

The complication aud difficulty of this treatment of the subject is avoided, with- 



92 SENIOR COURSE. 

out any appreciable error, by substituting for the sphere cones tangent to it at tlie 
circles of the pitch-sectors, and then developing these cones and treating them the 
same as spur-wheels. 

This will be best understood by making a drawing of a pair of bevel wheels 
1\" pitch, the pinion to have 15 teeth and the wheel 20. 

Draw the axes of the wheels at right angles to each other, and lay off the pitch- 
diameters, 5.968" and 7.958", as shown in Plate 43. Connect the extremities of these 
diameters with the intersection of the axes, for the pitch-cones. On these lines, 
lay off the length of the teeth, 2|", and draw perpendiculars extending to the 
axes. These perpendiculars will represent the tangent-cones ; that is, they will be 
tangent to the imaginary sphere and normal to the pitch-cones. The development of 
portions of these tangent-cones will result in arcs of circles, one pair for the outside 
end of the teeth, and the other pair for the inside end, which can then be treated pre- 
cisely as pitch-circles of spur-wheels, and involute or cycloidal teeth be generated upon 
them by any system desired. 

The actual production of theoretically correct teeth for bevel wheels is difficult, 
because every element of them should converge to the intersection of the axes. They 
can be produced by a reciprocating cutting point, one end of whose guide oscillates 
about the apex of the pitch-cone, while the other end is moved in the required path 
to produce the shape of the tooth. This was well illustrated by Mr. George H. 
Corliss' cycloidal bevel-gearing at the Centennial Exhibition of 1876, but is applica- 



MECHANICAL DRAWING. 93 

ble only to large teeth. Mr. Hugo Bilgram has discovered a principle, and invented 
a machine by which perfect involute teeth of small pitch can be cut. With ordinary 
machine-shop appliances, however, the best that can be done, in cutting teeth of bevels, 
is to make the flanks radial lines, and approximate the curve of the faces. This 
introduces another system of cycloidal teeth, which is equally applicable to spur-wheels 
when not required to be interchangeable. 

It has been shown that, if the rolling-circle is half the diameter of the pitch- 
circle, the resultant hypocycloid will be a radial line, and also that the proper epicy- 
cloid to work with this should be generated by the same rolling-circle, hence, if we 
roll on the outside of the developed arc of the tangent cone of the pinion, -a circle of 
half the diameter of the development of the tangent cone of the wheel, and vice versa, 
we will produce faces of proper cycloidal form to gear with the radial flanks. 

Draw the developed arcs of the tangent-cones and the rolling-circles, lay off the 
pitches, aud construct the shapes of the large end of the teeth as shown. 

The path of contact of the teeth comprises the portions of the arcs of the rolling- 
circles included within the addendum-circles as before, and it will be noted that the 
obliquity of action is less than in the system formerly explained, but that the 
action is confined to a smaller surface of the tooth, thereby causing more concen- 
trated wear and earlier distortion of the shape. The disadvantage of greater 
obliquity of action is more than counterbalanced by the additional wearing surface 
obtained by it. 



94 SENIOR COURSE. 

After generating the face of one tooth, find by trial the radius and centre of a 
circular arc to approximate it, and complete several teeth. 

The shape of the inside end of the teeth is produced in the same manner by 
developing the tangent-cones at that point. The pitch, addendum, depth, radius of 
approximate arc, and everything at the small end, are in the same proportion to those 
of the large end, as the distance from the apex to the pitch-point of the large end, is 
to the distance from the apex to the pitch-point of the small end. To find any of 
these, strike arcs from the apex as centre, tangent to both ends of the teeth, when any 
dimension laid oflf on the one, will be determined by a radial line cutting the other. 

The developed arcs of the tangent cones are to be treated precisely the same as 
pitch-circles of cylindrical gears of the same diameters as these arcs, and not as pitch- 
diameters of the bevel- wheels. The shape of tooth is to be produced in the same 
manner, limited and governed only by possibilities of construction. The student 
should draw bevel-gears in which the ratio of the pitch-diameters are different, and 
also a pair in which the axes are not at right angles, one pair with involute teeth 
(23°), and one with cycloidal teeth with curved flanks, after which no difficulty need 
be apprehended in handling the subject. 

Plate 43 is deficient in dimensions for shop use, both for turning the wheels and 
for cutting the teeth, although everything is fully determined as far as the drawing is 
concerned. For shop purposes there should be given the diameter of the outside 
corners and the angles of the outside and root of the teeth. 



MECHANICAL DRAWING. 95 



CONCLUSION. 



Any student who has carefully, accurately, and thoughtfully made the drawings 
of these Courses should, if he has had the advantage of any scientific or technical 
education, be capable of creditably handling any problem that might arise. The 
variety of these problems is infinite, but they can all be analyzed into comparatively 
simple details, and if the training derived from the examples which have been 
explained, tends to make the path easier in other or more difficult cases, the purpose of 
the books has been attained. 



96 



SENIOR COURSE. 



DECIMAL EQUIVALENTS 

OF 8THS, 16THS, 32DS, AND 64THS OF AN INCH. 



FRACTION 
of an inch. 


DECIMAL 
of an inch. 


FRACTION 
of an inch. 


DECIMAL 

of an inch. 


FRACTION 
of an inch. 


DECIMAL 
of an inch. 


FRACTION 
of an inch. 


DECIMAL 
of an inch. 


1 __ 

it — 


.015625 


17 


= .265625 


II 


= .515625 


49 

IT 


= .765625 


A = 


.03125 


9 
32 - 


= .28125 


II 


= .53125 


25 
32 


= .78125 


3 

IT 


.046875 


19 

IT - 


= .296875 


3 5 

IT 


= .546875 


5 1 

IT 


= .796875 


1-16 = 


.0625 


5-16 = 


= .3125 


9-16 


= .5625 


13-16 


= .8125 


A = 


.078125 


21 
IT - 


= .328125 


37 
IT 


= .578125 


53 

IT 


= .828125 


3 


.09375 


11 


= .34375 


1 9 
¥2 


= .59375 


it- 

¥2 


= .84375 




.109375 


23 _ 

IT - 


= .359375 


39 

IT 


= .609375 


5 5 

IT 


= .859375 


1-S = 


.125 


3-8 = 


= .375 


5-8 


= .625 


vs 


= .875 


9 

IT — 


.140625 


25 _ 
IT - 


= .390625 


41 
6T 


= .640625 


57 
IT 


= .890625 


A = 


.15675 


11 - 

32 


= .40625 


21 
32 


= .65625 


29 
■J2 


= .90625 


ii 

IT — 


.171875 


27 - 
IT - 


= .421895 


43 

IT 


= .671875 


5 9 
IT 


= .921875 


3-16 = 


.1875 


7-16 = 


= .4375 


11-16 


= .6875 


15-16 


= .9375 


if = 


.203125 


29 _ 
IT - 


= .453125 


4 5 

ST 


= .703125 


61 
IT 


= .953125 


A = 


.21875 


15 _ 
¥2 - 


= .46875 


23 

T2" 


= .71875 


3 1 
32 


= .96875 


15 

IT — 


.234375 


31 - 

IT - 


= .484375 


47 
IT 


= .734375 


63 

IT 


= .9S4375 


1-4 = 


.25 


1-S = 


= .5 


3-4 


= .75 







MECHANICAL DRAWING. 



97 



STANDARD PROPORTIONS FOR BOLTS AND NUTS. 



Diameter 


Threads 
per inch. 


Diameter at 


Width 


Short Diameter 


Long Diameter 


Thickness of 


Diameter 


Thickness 


of 


Root of 


of 


of Head 




of 


Head 


of 




of 


Screw. 


Thread. 


Flat. 


and Nut 




Hexagon. . 


and Nut. 


Washer. 


Washer. 


1 

4 


— 20 — 


— .185 — 


— .0062 — 


- A 


_ 


— .505 — 


- A~ 


9 

16" 





3 

■J2 


T6~ 


— 18 — 


— .240 — 


— .0074 — 


3 2 


— 


— .613 — 


i 

4 


1 1 
1 6 


— 


i - 


3 
8 


— 16 — 


— .294 — 


— .0078 — 




— 


— .722 — 


5 
8 


13 

T6 


— 


i - 


1 S 


— 14 — 


— .344 — 


— .0089 — 


23 

"3 2 


— 


— .830 — 


15 

1 6 


— 


i - 


1 
— 2~ — 


— 13 — 


— .400 — 


— .0096 — 


A3 

16 


— 


— .938 — 


- A- 


- 1A - 


— 


A- 


9 


— 12 — 


— .454 — 


— .0104 — 


29 
3 2 


— 


— 1.046 — 


- $ - 


- 1A - 


— 


3 

T6 — 


- 1 - 


— 11 — 


— .507 — 


— .0113 — 


— 1 


— 


— 1.154 — 


9 

76 


1_5 

x l 6 


— 


3 

T6 — 


a 

4 


— 10 — 


— .620 — 


— .0125 - 


- 1t 3 o 


— 


— 1.371 — 


1 1 
IS 


1 9 

— Are — 


— 


i - 


7 


— 9 • — 


— .731 — 


— .0138 — 


- H 


— 


— 1.587 — 


13 

TB" 


113 

— Its — 


— 


I - 


— 1 — 


— 8 — 


— .837 — 


— .0156 — 


19 

X TS 


— 


— 1.804 - 


1 5 
1 6 


91 


— 


5 
T5 


- H - 


— 7 — 


— .940 — 


— .0178 — 


11 

l 4 


— 


— 2.020 — 


- 1A — 


2_5 

■^1 6 


— 


5 

T6" 


- n - 


- 7 — 


— 1.065 — 


— .0178 — 


- m 


— 


— 2.237 — 


- 1A - 


2_9 

•''I 6 


— 


5 

T6" — 


- H - 


— 6 — 


— 1.160 — 


— .0208 — 


— n 


— 


— 2.453 — 


1 5 

X T6 


91 3 

^1 6 


— 


5 

To" — 


- u - 


— 6 — 


— 1.284 — 


— .0208 — 


— ?A 


— 


— 2.670 — 


1_7 

a 1 6 


3 T 7J 


— 


5 

T6 — 


- if - 


- 5i - 


— 1.389 — 


— .0227 — 


— n 


— 


— 2.886 — 


1 9 


- 3A — 


— 


A 

8 ^^ 


- if - 


— 5 — 


— 1.491 — 


— .0250 — 


Ol 1 


— 


— 3.103 — 


111 


Q 9 

— °TS — 


— 


3 

8 


- ij - 


— 5 — 


— 1.616 — 


— .0250 — 


^8 


— 


— 3.319 — 


_ 111 

1 1 6 


Q13 

°TS 


— 


8 

8 


— 2 — 


- 4£ — 


— 1.712 — 


— .0277 — 


Q 1 

— "T8~ 


— 


— 3.536 — 


115 


4_i 

M 6 


— 


3 

8 


- 2J - 


— 4J — 


— 1.962 — 


— .0277 — 


— 3-V 

To 


— 


— 3.969 — 


— 2A - 


4 9 


— 


1 

f 


ok 


— 4~ — 


— 2.176 — 


— .0312 — 


— m 


— 


— 4.402 — 


- 2 T % — 


^ 1 
— °T6 — 


— 


1 

2 — 


- 2} - 


— 4 — 


— 2.426 — 


— .0312 — 


— *A 


— 


— 4.835 — 


911 

^T6 


- 5& - 


— 


i — 


— 3 — 


- 3| - 


— 2.629 — 


— .0357 — 


- *h 


— 


— 5.268 — 


_ 919 


- 6A - 


— 


i - 



98 SENIOR COURSE. 

WROUGHT-IRON WELDED STEAM, GAS, AND WATER PIPE. 



TABLE OF STANDA1U) SIZES AND DIMENSIONS. 



2 

c C 

J J 


13 . 

^ d 

13 


r3 


^4 


a 

u 

s . 


u 

s 

F a 


angth of Pipe 
per Square foot 
of Inside Sur- 
face. 


ength of Pipe 
per Square foot 
of Outside Sur- 
face. 


G3 

a 
u 


u 
< 

1 


*o . 

fci. = "Z 


ominal "Weight 
per foot of 
Length. 


% ° 

c u u 
6 £.«) 




z 


<! 


<1 


H 


M 


W 


►J 


►-1 


w 


A 


£ 


fc 





Inches. 


Inches. 


Inches. 


Inches. 


Inches. 


Inches. 


Feet. 


Feet. 


Sq. Ins. 


Sq. Ins. 


Feet. 


Pounds 




Gallons. 


Va 


.27 


.40 


.07 


.84 


1.27 


14.15 


9.44 


.00 


.12 


2500. 


.24 


27 


.002 


A 


.30 


.54 


.08 


1.14 


1.09 


10.50 


7.07 


.10 


.22 


1385. 


.42 


18 


.002 


7* 


.49 


.07 


.09 


1.55 


2.12 


7.07 


5 05 


.19 


!»5 


751.5 


.50 


18 


.005 


y% 


.02 


.84 


.10 


1 95 


2.05 


6.13 


4 50 


.30 


.55 


472.4 


.84 


14 


.010 


% 


.82 


1.05 


.11 


2 58 


3.29 


4,03 


3.03 


.53 


.86 


270. 


1.12 


14 


.023 


\ 


1.04 


1.31 


.13 


3.29 


4.13 


3.07 


2.90 


.86 


1.35 


100.9 


1.07 




.040 


Hi 


1.38 


1.66 


.14 


4 33 


5.21 


2.70 


2,30 


1.49 


3 10 


90.25 


2.24 


.063 


1.61 


1.9 


.14 


5.00 


5.90 


2.37 


2 01 


2.03 


2.83 


70.05 


2 08 


i'K 


.091 


2 


2.06 


2.37 


.15 


0.49 


7.40 


1.84 


1.01 


3.35 


4.43 


42.36 


3.61 


»% 


.103 


2 ^ 


2.46 


2.87 


.20 


7.75 


9.03 


1.54 


1.32 


4.78 


6.49 


30.11 


5.74 


8 


.255 


3 


3.00 


3.5 


.21 


9.03 


10.90 


1.24 


1 09 


7.38 


9.02 


19 49 


7.54 


8 


.307 


314 


3.50 


4. 


.22 


11.14 


12.56 


1.07 


.95 


9.83 


12.56 


14 50 


9 00 


8 


.500 


4 


4.02 


4.5 


.23 


12.04 


14.13 


.94 


.84 


12 73 


15.90 


11.31 


10 00 


8 


.652 


4 V£ 


4.50 


5. 


.24 


14.15 


15.70 


.84 


.70 


15.93 


19.63 


9.03 


12.34 


8 


.826 


5 


5.04 


5.56 


.25 


15.84 


17.47 


.75 


.62 


19 99 


24.29 


7.20 


14.50 


8 


1.02 


6 


6.06 


6.62 


.28 


19.05 


20.81 


.03 


.57 


2S.88 


3447 


4.98 


IS. 70 


8 


1.46 


7 


7.02 


7.62 


.30 


22.00 


23 95 


.54 


.50 


38.73 


45 00 


3.72 


23 27 


8 


2.00 


8 


7.98 


8.62 


.32 


25.07 


27.09 


.47 


.14 


50.03 


58.42 


2 88 


28.18 


8 


2.61 


9 


9.00 


9.68 


.34 


28.27 


30.43 


.42 


.39 


03.03 


73.71 


2.20 


33.70 


8 


3.30 


10 


10.01 


10.75 


.36 


31 47 


33.77 


.38 


.35 


78 83 


90 79 


1.80 


40.00 


8 


4.08 


11 


11. 


11.75 


.37 


34.55 


30 91 


.34 


.32 


95.03 


IDS 43 


1 50 


45. 


8 


4 93 


12 


12. 


12.75 


.37 


37.70 


40 05 


.32 


.30 


113.09 


127.67 


1.27 


48.98 


8 


5.87 


13 


13.25 


14. 


.37 


41.02 


43.98 


.29 


.27 


137 88 


153.94 


1.04 


53.92 


8 


6.89 


14 


14.25 


15. 


.37 


44.70 


47.12 


.27. 


.25 


159 18 


170.71 


.90 


57.89 


8 


8.00 


15 


15 40 


16. 


.28 


48.48 


50.20 


.25 


.24 


187.04 


201.00 


.77 


66.00 


8 


9.18 


IB 


10.40 


17. 


.30 


51.52 


53.41 


- .23 


.23 


211 24 


220.98 


.08 


7O.00 


8 


10.44 


17 


17.30 


18. 


.34 


54.41 


50.55 


.22 


.21 


235.01 


254.47 


.61 


75.00 


8 


11.79 



MECHANICAL DRAWING. 

PROPORTIONS OF TEETH OF GEARS. 



99 



No. of 
Teem per 
inch of 
Diam'ter 



12 

11 

10 

9 

8 

7 



5 
4 
31 



i 

.2618 
.2856 
.31416 
.34906 

3 
8 

.3927 
.4477 

1 
.5236 



.62832 

a 

i 

.7854 



.89714 

1 



Addendum 
outside of 

Pitch Line 
(.3 pitch). 



.075 
.079 
.086 
.094 
.104 
.113 
.118 
.134 
.150 
.157 
.169 
.188 
.189 
.225 
.236 
.262 
.269 
.300 



Depth inside 

of 
Pitcli Line 
(.35 pitch). 



.0875 

.0916 

.0999 

.1099 

.1221 

.1312 

.1374 

.1567 

.175 

.1833 

.1969 

.2187 

.2199 

.2625 

.2749 

.3062 

.3140 

.35 



Pitch 
Diarn equals 
No. of Teeth 
Multiplied by 



.079577 
i 

T2 

1 
Tl 



.119366 

* 

i 

7 

.159155 
i 

.179049 

.198944 

i 

■5" 

.238732 
i. 

4 

.278521 

2 

7 

.31831 



No. of Teeth 
per inch 

of 
Diameter. 



3 

2| 

21 



14 



Pitch. 


Addendum 
outside of 

Pitch Line 
(.3 pitch). 


Depth inside 

of 
Pitch Line 
(.35 pitch). 


Pitch 
Diam. equals 
No. of Teeth 
Multiplied by 


1.0472 


.314 


.3665 


i 


i* 


.338 


.3937 


.358099 


1.1424 


.343 


.3998 


4 

11 


l£ 


.375 


.4375 


.397887 


1.25664 


.377 


.4398 


2 

5 


If 


.413 


.4812 


.437676 


11 


.450 


.525 


.477465 


1.5708 


.471 


.5498 


i 


If 


.525 


.6125 


.557042 


2 


.600 


.70 


.63662 


2.0944 


.625 


.7330 


t 


21- 


.675 


.7875 


.716197 


21 


.750 


.875 


.795775 


2| 


.825 


.9625 


.875352 


3 


.900 


1.05 


.95493 


3.1416 


.942 


1.0995 


1 


31 


.975 


1.1375 


1.034047 


31 


1.050 


1.225 


1.114085 



100 



SENIOR COURSE. 



Table for the Shapes of Gear-Teeth of One Inch Pitch by Approximate Circular Arcs. 

MULTIPLY THESE FIGVJRES BY THE PITCH IN INCHES. 



INTERVALS OF 


INVOLUTE. 


CYCLOIDAL. 


CUTTERS. 


Centres on 230 Line of Action. 




Faces. 


Flanks. 








Maximum 
Radius 
























Exactly 

correct for 
No. of Teeth. 


Approximately 

correct for 
No. of Teeth. 


Radius 

of 
Face. 


Radius 

of 
Flank. 


of 
Fillet. 


Radius. 


Distance of 
centre inside 
of Pitch Line. 


Radius. 


Distance of 
centre outside 
of Pitch Line. 


12 




.950 


.668 


.15 


.59 


.016 


oo 


OO 


13 




1.020 


.713 


.15 


.62 


.02 


5.78 


4 00 


14 




1.090 


.758 


.125 


.64 


.02 


4.38 


2.70 


15 




1.160 


.803 


.125 


.66 


.025 


3.83 


2.22 


16 




1.229 


.848 


.125 


.68 


.03 


3.40 


1.80 


17 




1.299 


.893 


.125 


.685 


.03 


2.65 


.93 


18 




1.368 


.938 


.125 


.695 


.03 


2.26 


.83 


20 


19- 21 


1508 


1.028 


.1 


.70 


.03 


1.84 


.56 


23 


22- 24 


1.717 


1.163 


.1 


.72 


.04 


1.60 


.41 


27 


25- 29 


1.995 


1.343 


.075 


.73 


.04 


1.50 


.34 


33 


30- 36 


2.413 


1.613 


.05 


.76 


.045 


1.42 


.30 


42 


37- 48 


3.040 


2.017 


.0375 


.77 


.05 


1.25 


.22 


58 


49- 72 


4.154 


2.736 


.0375 


.83 


.065 


1.04 


.13 


97 


73-144 


6.870 


4.190 


.0375 


.90 


.075 


1.00 


.12 


200 


145-300 


14.042 


9.02 


.0375 


.91 


.08 


.96 


.11 


Eack 




QO 


oo 


.0375 


.92 


.09 


.92 


.09 



Differences of radii for each involute tooth, — face, .07 ; flank, .045. 



IND KX. 



PAGE 

Addendum, 71, 75, 79, 99 

Admission of steam, 50, 52, 59 

Angle of action of gear-teeth, 72, 74, 79 

" " advance of eccentric, . . . . 38,42,50,53,56,01 

" " obliquity of teeth, 72, 79, 82, 90 

" " tangent of helix, 13, 15 

" " crank, 52, 60 

Angularity of connecting-rod, 60 

" " eccentric-rod, 63 

Approximate shapes for gear-teeth, .... 77,81,89,100 

Arc of approach of teeth 73 

" recess of teeth 73 

Arms of gear-wheels 85 

Base-circle of gear-wheels, 70 

Base-lines, 10, 57 

Bevel gear-wheels, 90 

Bilgram valve diagram 55 

Black forgings, 33 

Blue Prints, 10 

Bolts, 20,32 

" black 33 

" conventional drawing of 24 

" list of, 34 



Bolts, proportions for 

" round-head, 

" standard shape of thread of, . 

" stud, 

" tap, 

" thiough, 

Brass details, 

Broken length to accommodate paper, 

Bushing 

Caps for bearings, 

Cast-Iron, section lines for, 

Clearance for gear-teeth, 

" of steam piston, 

" space in steam cylinder, . . 

Compression of steam, 

" equalization of, 

Connecting-rod, 

" adjustable 

" angularity of, ... . 

Construction drawing 

Counterbalancing reciprocating parts, 
Covers for cylinder and steam-chest, . 
Crank-angle, 



PAGE 


21 


33 




34 




21 


32,44 


46 




32 


32 


46 




43 




36 


39,43 


46 




45 




19 




78 




45 




50 


54 


59 




61 


36 


43 




65 




60 


27 


48 


3S 


40 




44 


52 


GO 



101 



102 



INDEX. 



PAGE 

Crank-shaft, 37 

Ciosshead, 41 

Cut-off, 53,59 

" equalization of, 60 

Cycloid, 87 

Cyc'oidal gear-teeth, 86 

Cylinder, 45 

" head, 44 

Decimal equivalents, 76, 96 

Designing of valve motion, 62 

Details, names of, 27 

" numbers for 28,29 

" scale of, 30 

Development of helix, 12 

" tangent cones of bevel gears, 92 

Diagram, valve, 55 

Diameter of wheels, pitch 75,84,91 

" '* outside, 75, 84 

" " root, 75,84 

Diametral pitch, 83 

Directrix, 14 

Dowel-pins, . . . , 32, 45 

Eccentric, 42, 52, 56 

" angular advance of, . . . . 38,42,50,53,56,61 

" throw, 42, 59 

Engine, Bilgram valve diagram for, 55 

" bolts and keys for, 32 

" brass details of, 43 

" connecting-rod for, 36, 43, 65 

" construction drawing of, 27,48 

*' covers nnd caps for 45 

" crank-shaft for 37 



PAGE 

Engine, crosshead for, 41 

" cylinder for, 45 

" eccentric and strap for, 42 

" eccentric-rod for, 36, 65 

" fly-wheel for, 40 

" frame for, 47 

" gland, bushing and brasses for, ... 39, 43 

" list of bolts for, 29,34 

" pieces for 28 

" piston for, 39 

" piston-rod and pins for, 35 

" piston-rings for 35 

" slide-valve for, 41 

" valve motion of, 51, 55 

Epicycloid, 87 

Equalization of cut-off, 60 

" " exhaust, 61 

" lead 60 

" release and compression, . . 61 

Exhaust lap 52 62 

Expansion of steam, 54, 60 

Face of gear-teeth, 71 

width of, 85,92 

Fillets 37, 78, 100 

Fixed point of Bilgram valve diagram, ... 57 

Finished forgings, 33 

Flank of gear-teeth, 71, 77 

Fly-wheel 40 

Gear-teeth, addendum of, 71,75 

" clearance for, 78 

depth of, 75^9 

" diametral pitch of, 83 



INDEX. 



103 



PAGE 

Gear-teeth, efficiency of, 74, 80, 93 

" errors liable to occur in cutting, . 80 

«' face of, 71, 77 

fillets for, 78, 100 

" flank of, 71,77,93 

" for rack 76, 79 

" intervals of cutters for 82, 100 

" pitch of, 70, 75 

" pitch point of, 70, 77 

" width of face of, 85,92 

" cycloidal 80 

" " approximate 89, 94, 100 

" " for bevel wheels, ... 91 

*• " path of contact of, . . 89 

" " rolling circle for, ... 87 

" " to describe, 88 

" involute 70, 75, 77 

" " approximate 77, 81, 100 

" ' " base circle for, 70 

" " interchangeable, ... 81 

" " line of action of, ... . 70, 76 

" " locus of centres for arcs of 83 

" " obliquity of action of, . 74 

" " path of contact of, . . . 70, 72, 79 

" " reasonsfor superiority of, 80, 90 

" " to describe 77 

Gear-wheels, bevel SO 

•' " developed arcs of, ... . 92 

" " pitch circles of, 91 

" " pitch diameters of, .... 91 

" " tangent cones of 92 

*' spur 67 



PAfiE 

Gear-wheels, spur, pitch Jiameters of, . . . . 75,84 

" outside diameters of, . . 75, 84 

" root diameters of, .... 75, 84 

" proportions for 85 

Generatrix, 14, 17 

Gland, 39,43,46 

Globe valve, 66 

Helicoid 14 

Helix, 11 

" pitch of, 11. 15 

" angle of, 13 

" development of 12 

High face for fly-wheels 40 

Hypocycloid, 87 

Individual pitch of screws, 16 

Inking 10, 30 

Inside lap, 52, 62 

Intervals of cutters for teeth, 82,100 

Interchangeable gear wheels, 81, 88 

Involute, 69, 77 

" point of origin of, 77 

" by approximate circular arcs, ... 77. 100 

" teeth for gear wheels, 69,75 

Joint, rubber, .• . 44 

Keys, 32,65 

Key-seats, 38,41,42 

Lead of slide-valve, 50, 52, 60 

Lap, exhaust, 52,62 

" inside 52, 02 

" negative, 52 

" outside, 51 

" steam, 51, 61 



104 



INDEX. 



PAGE 

Lap, circle, 5C, 59 

Left-hand screw threads, 19 

Lines, rules for inking 10,30 

Line of centres of gear wheels, G8 

" action of teeth 70,76,79,93 

Motion, valve, 51, 55 

Multipk- threads, 16 

Names for details, 27 

Negative lap, 52 

Numbers for details 28, 29 

Number of teeth in wheels, smallest, . . . .72,74,79,88 

Nut for screw-thread, 15 

Nuts for bolts 21, 23, 33 

Obliquity of action of gear teeth 74,79,82,90,93 

Oil holes, 35, 36, 40, 42, 43 

" cup, 44 

Paper, size of, 10, 30, 49, 75 

Path of contact, 70, 72, 89, 93 

Pins for crosshead and valve stem, 35 

" dowel 32, 45 

" split 35 

Pipe threads, 25 

Pipes, drain, 46, 50 

Piston, ...» 39 

" rings, 35, 39 

" rod 35 

Pitch circle, 70, 76 

" cone, 90 

" cylinder, 70 

" diameter, 75, 84, 91 

" diametral S3 

" of gear teeth 70, 75 



PAGE 

Pitch of screw threads, 11, 15, 16, 21 

" point 70, 77, 91 

Port, exhaust, 46, 53 

" opening 56, 59, 62 

" steam, 46 

Proportions for bolts 21 

" " gear wheels, 85 

" " pipes 25, 98 

" " square threads, 16, 18, 20 

Rack, teeth of, 76,79 

Ratio, velocity, 68 

Release of steim, . 59 

Right-hand screw threads, 19 

Rim of gear wheels, thickness of, 86 

Rings for piston, 35 

Rolling circle for cycloidal teeth 87 

" " tteth of bevel wheels, . . . 91,93 

Root diameter of gear wheels, 75, S4 

Scales, drawing 7,9,30,49,56 

Screws, efficiency of, 15 

Screw threads, conventional, 18, 19, 24 

" " individual pitch of, 16 

" " multiple 16 

" " proportions of, 16, 18, 20, 21, 97 

" " right or left hand 19 

Section lines for brass 39 

" " cast iron, 19, 41 

" " wrought-iron and steel, . . . 19,36 

Shop drawings, 26 

Slide-valve, 41 

Split pins 35 

Steam chest, 46 



INDEX. 



105 



Steam cylinder, 

" lap, 

Pipe, 

" port, 

Steel, 

Tangent of helix, 

" cones of bevel wheels, 

Taper of arms, 

" fly-wheel face, .... 

" hole, 

" keys, 

" rods, 

Teeth of wheels, bevel, 

" " cycloidal, . . 
" " involute, . . . 



PAGE 

45 

51, 61 

25,46 

46,53 

19 

13 

92 

86 

40 

39 

65 

35 

92 

88 

70, 77 



Threads, bolt 

pipe, 

" screw, 

Titles of drawings, 

Valve globe, 

" rod, 

" seat, 

" slide, 

" motion, 

" " designing of, . 

Vertical engine, ..... . 

Velocity ratio of gear wheels, 

Washers, 

Working drawings, 



14 



PAGE 

21,34 

25 

16,21 

30 

66 

35 

46 

41 

51,55 

62 

26,27 

87,91 

24 



Plate 21. 




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